Download Sample Distributions

Name: ________________________ Class: ___________________ Date: __________
ID: A
Sample Distributions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which of the following is not an example of a discrete random variable?
a. the number of heads observed for ten coin tosses
b. the mass of an apple randomly chosen from a supermarket bin
c. the sum resulting from the roll of two six-sided dice
d. the number of hearts in a randomly chosen hand of seven playing cards
____
2. A tetrahedron has four equal triangular faces. The faces of a tetrahedral die are labelled with the numbers one,
three, five, and seven. What is the expected value of the random variable representing the number observed on a
single roll of this die?
a. 3
c. 4
b. 3.5
d. 5
____
3. What is the probability of a sum of 5 resulting from the roll of two six-sided dice?
5
1
a.
c.
36
18
1
1
b.
d.
9
36
____
4. When we compare the possible values for a discrete random variable to its expected value, the following
statement must be true.
a. The possible values and the expected value must all be whole numbers.
b. The expected value must be one of the possible values.
c. The possible values must all be whole numbers but the expected value may be a rational
number.
d. The expected value will not be a whole number.
____
5. The probability of drawing a red card from a deck of 52 playing cards is 0.5. Which of the following
statements is not necessarily true?
a. The expected value for the number of red cards in a 7 card hand will be 3.5.
b. Over many repeated drawings you would expect the ratio of red cards drawn to total
number of drawings to be close to 1:2.
c. The expected value for the number of black cards in an 8 card hand will be 4.
d. If you successively draw and replace a card 100 times, you will see 50 red cards.
____
6. What is the probability of rolling less than 3 on a single roll of a six-sided die?
1
1
c.
a.
3
6
1
2
b.
d.
2
3
1
Name: ________________________
____
ID: A
7. A game is played by spinning a wheel that is divided into four sectors, each with a different point value. The
central angle and point value for each sector is shown in the chart below.
Central Angle
144°
108°
72°
36°
Point Value
20
30
40
50
How many total points would you expect to get for 100 spins of the wheel?
a. 3500
c. 2500
b. 3000
d. 2000
____
8. Which of the following is an example of a discrete random variable?
a. the time needed by a student to complete a physics lab
b. the number of red cars observed in a student parking lot
c. the mass of a green pepper selected at random from a bin
d. the cost of a U.S. dollar in Canadian currency on a given day
____
9. The following table shows the probability distribution for the possible sums that result from rolling two 6-sided
dice.
X
1
P(X)
0
X
7
P(X)
6
8
36
5
2
1
3
36
2
9
36
4
4
36
3
10
36
3
5
36
4
11
36
2
6
36
5
12
36
1
36
36
What is the probability that the sum rolled is even and less than 9?
7
1
a.
c.
18
9
5
1
b.
d.
36
2
2
Name: ________________________
ID: A
____ 10. What is the probability of drawing exactly 2 red cards in a hand of 3 cards drawn from a deck of 52 cards?
1
2
a.
c.
8
3
1
3
b.
d.
2
8
____ 11. A game involves tossing three coins. If two or more of the coins are heads, the player wins a prize. Each play
costs $0.25. What value of prize will make this a fair game?
a. $0.40
c. $0.45
b. $0.50
d. $0.38
____ 12. The following table is a valid probability distribution for a random variable X. What must be the value for P(2)
to complete the table?
X
0
1
2
3
a.
b.
P(X)
0.15
0.2
0.4
0.15
0.2
c.
d.
0.25
0.3
____ 13. A random variable X is defined as the number of heads observed when a coin is tossed 4 times. The probability
distribution for this random variable is shown below.
X
P(X)
0
1
1
4
2
6
3
4
4
1
16
16
16
16
16
Which of the following statements is not true?
a. The probability of no heads is the same as the probability of 4 heads.
b. The most likely outcome is 2 heads.
6
c. The expected value is .
16
d. The probability of not tossing 2 heads is greater than the probability of tossing 2 heads.
____ 14. What is the expected value for a single roll of a 6-sided die?
a. 3.5
c. 4
1
b. 3
d.
6
3
Name: ________________________
ID: A
____ 15. A student is preparing a probability distribution as shown below.
X
0
1
2
3
4
P(X)
0.3
0.3
0.3
0.3
A value is needed for P(3) to complete the table. Which statement below is true?
a. The required value for P(3) is 0.3.
b. The required value for P(3) is 0.2.
c. The required value for P(3) is –0.2.
d. There is no possible value for P(3) that can make this a valid probability distribution.
ÊÁ ˆ˜
ÁÁ n ˜˜
____ 16. According to Pascal’s Identity, the single expression of the form ÁÁÁÁ ˜˜˜˜ , which is equivalent to
ÁÁ ˜˜
Ër¯
ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ 11 ˜˜
ÁÁ 12 ˜˜
Á
˜
a. ÁÁÁ ˜˜˜
c. ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜
ÁÁ ˜˜
Ë 5¯
Ë 4¯
ÊÁ ˆ˜
ÊÁ
ˆ
ÁÁ 12 ˜˜
ÁÁ 121 ˜˜˜
Á
˜
Á
˜˜
b. ÁÁÁ ˜˜˜
d. ÁÁÁ
˜˜˜
ÁÁ ˜˜
ÁÁ
˜
3
12
Ë ¯
Ë
¯
ÁÊÁ ˜ˆ˜
Á8˜
____ 17. According to Pascal’s Identity, what two expressions may be added to obtain ÁÁÁÁ ˜˜˜˜ ?
ÁÁ ˜˜
Ë6¯
ÊÁ ˆ˜ ÊÁ ˆ˜
ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 4 ˜˜ ÁÁ 4 ˜˜
ÁÁ 8 ˜˜ ÁÁ 8 ˜˜
Á
˜
Á
˜
a. ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜
c. ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜ ÁÁ ˜˜
Ë 3¯ Ë 3¯
Ë 4¯ Ë 5¯
ÊÁ ˆ˜ ÊÁ ˆ˜
ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 7 ˜˜ ÁÁ 7 ˜˜
ÁÁ 7 ˜˜ ÁÁ 7 ˜˜
Á
˜
Á
˜
b. ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜
d. ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜ ÁÁ ˜˜
Ë 5¯ Ë 6¯
Ë 4¯ Ë 5¯
7
____ 18. How many terms are in the expansion of ÊÁË 2x − 3y ˆ˜¯ ?
a. 5
c. 7
b. 8
d. 6
5
____ 19. In the expansion of ÊÁË x + y ˆ˜¯ , what is the coefficient of the fourth term?
a. 10
c. 7
b. 4
d. 5
4
ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 11 ˜˜ ÁÁ 11 ˜˜
ÁÁ ˜˜ + ÁÁ ˜˜ ?
ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜ ÁÁ ˜˜
Ë 3¯ Ë 4¯
Name: ________________________
ID: A
n
____ 20. In the expansion of ÊÁË x + y ˆ˜¯ , which term or terms must have coefficients with a value of n?
a. none
c. the middle term or middle two terms
b. the second term
d. the second and second from last terms
ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜
ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜ ÁÁ 5 ˜˜
____ 21. What is the value of ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ + ÁÁÁÁ ˜˜˜˜ ?
ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜
Ë 0¯ Ë 1¯ Ë 2¯ Ë 3¯ Ë 4¯ Ë 5¯
a. 30
c. 32
b. 64
d. 20
____ 22. In the expansion of (a + b ) , what is the value of the exponent k in the term that contains a 5 b k ?
a. 5
c. 4
b. 56
d. 3
8
ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜ ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ n ˜˜ ÁÁ n ˜˜ ÁÁ n ˜˜ ÁÁ n ˜˜
ÁÁ n ˜˜
Á
˜
Á
˜
Á
˜
Á
˜
____ 23. If ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜ + ÁÁÁ ˜˜˜ +. . .+ ÁÁÁÁ ˜˜˜˜ = 64, what is the value of n?
ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜ ÁÁ ˜˜
ÁÁ ˜˜
Ë 0¯ Ë 1¯ Ë 2¯ Ë 3¯
Ën¯
a.
b.
6
8
c.
d.
4
5
____ 24. What is the coefficient of the third term in the expansion of (3x + 1) ?
a. 10
c. 150
b. 15
d. 270
5
ÊÁ ˆ˜
ÁÁ 5 ˜˜
5−rÊ ˆr
Á y ˜ is the general term in the expansion of which binomial power?
____ 25. ÁÁÁÁ ˜˜˜˜ (2x)
Ë ¯
ÁÁ ˜˜
Ër¯
a.
b.
r
ÁËÊ 2x − y ˆ˜¯
5
ÁËÊ 2x + y ˆ˜¯
c.
d.
5
ÁËÊ 2x − y ˆ˜¯
ÊÁ 2x + y ˆ˜ r
Ë
¯
____ 26. Pascal’s Triangle can be arranged into the following format.
n=0
n=1
n=2
n=3
n=4
r=0
1
1
1
1
1
r=1
r=2
r=3
r=4
1
2
3
4
1
3
6
1
4
1
Which of the following statements is not true?
a. The sum of the nth row must be 2 n .
b. The value in any cell is the sum of the cell directly above and the cell above and one left.
c. Values in each row must alternate between even and odd numbers.
d. In any row for which n is prime, all values in the row other than the first and last must be
divisible by n.
5
Name: ________________________
ID: A
6
____ 27. For the expansion of ÊÁË 3x + y ˆ˜¯ , which statement is not true?
a. The coefficient of the term containing y 6 is one.
b. The coefficient of the second term is equal to the coefficient of the fifth term.
c. The degree of each term in the expansion is 6.
d. There are seven terms in the expansion.
ÁÊÁ
____ 28. What is the value of the constant term in the expansion of ÁÁÁÁ x 2 +
ÁË
a. 4
c. 16
b. 8
d. 32
6
2 ˜ˆ˜˜
˜˜ ?
x ˜˜¯
____ 29. How many different paths will spell the word CASH using the diagram below?
C
A A
S S S
H H H H
a.
b.
6
4
c.
d.
8
10
____ 30. Which of the following is a correct expression of Pascal’s Identity?
ÁÊÁ
˜ˆ ÁÊ
˜ˆ ÁÊ ˜ˆ
ÁÊÁ
˜ˆ ÁÊ
˜ˆ ÁÊ ˜ˆ
ÁÁ n − 2 ˜˜˜ ÁÁÁ n − 1 ˜˜˜ ÁÁÁ n ˜˜˜
ÁÁ n − 1 ˜˜˜ ÁÁÁ n − 1 ˜˜˜ ÁÁÁ n ˜˜˜
Á
˜
Á
˜
Á
˜
Á
˜
Á
˜˜ = ÁÁ ˜˜
a. ÁÁ
c. ÁÁ
˜˜ + ÁÁ
˜˜ = ÁÁ ˜˜
˜˜ + ÁÁ
˜˜ ÁÁ ˜˜
ÁÁ
˜˜ ÁÁ
˜˜ ÁÁ ˜˜
ÁÁ
˜˜ ÁÁ
˜ Á ˜
Ë r−2¯ Ë r−1¯ Ë r ¯
Ë r−1¯ Ë r ¯ Ë r ¯
ÊÁ
ˆ Ê
ˆ Ê
ˆ
ÊÁ ˆ˜ ÊÁ
ˆ Ê
ˆ
ÁÁ n + 1 ˜˜˜ ÁÁÁ n + 1 ˜˜˜ ÁÁÁ n + 2 ˜˜˜
ÁÁ n ˜˜ ÁÁ n ˜˜˜ ÁÁÁ n + 2 ˜˜˜
Á
˜
Á
˜
Á
˜
Á
˜
Á
˜
Á
˜˜
b. ÁÁÁ
d. ÁÁÁ ˜˜˜ + ÁÁÁ
˜˜˜ + ÁÁÁ
˜˜˜ = ÁÁÁ
˜˜˜
˜˜˜ = ÁÁÁ
˜˜
ÁÁ
˜˜ ÁÁ
˜˜ ÁÁ
˜˜
ÁÁ ˜˜ ÁÁ
˜˜ ÁÁ
˜˜
r
−
1
r
r
+
1
r
r
+
1
r
+
1
Ë
¯ Ë
¯ Ë
¯
Ë ¯ Ë
¯ Ë
¯
____ 31. Which of the following is not a property of a Binomial Experiment?
a. All trials are identical.
b. Each trial has only two possible outcomes.
c. The probability of success may change from trial to trial.
d. The purpose of the experiment is to determine the number of successes that occurs during
the n trials.
____ 32. Which of the following is not an example of a Bernoulli Trial?
a. A coin is tossed 20 times and the number of heads is recorded.
b. A container contains 49 numbered balls. Six are drawn one at a time from the container.
c. A couple produces 18 children. The number of female children is recorded.
d. A batter has a lifetime average of .300. The number of hits in 5 successive at-bats is
recorded.
6
Name: ________________________
ID: A
ÁÊÁ ˜ˆ˜
Á 8˜
3
5
____ 33. In the expression ÁÁÁÁ ˜˜˜˜ (0.2) (0.8) , which value represents the number of trials?
ÁÁ ˜˜
Ë 3¯
a. 2
c. 5
b. 3
d. 8
ÊÁ ˆ˜
ÁÁ 7 ˜˜
2
5
____ 34. In the expression ÁÁÁÁ ˜˜˜˜ (0.4) (0.6) , which value represents the probability of failure?
ÁÁ ˜˜
Ë 2¯
a.
b.
0.6
0.4
c.
d.
(0.4)2
(0.6)5
ÊÁ ˆ˜
ÁÁ 10 ˜˜
3
7
____ 35. In the expression ÁÁÁÁ ˜˜˜˜ (0.5) (0.5) , which value represents the number of successes?
ÁÁ ˜˜
Ë 3¯
a. 3
c. 5
b. 10
d. 7
____ 36. Which expression describes the probability of k “3s” being rolled on 20 successive rolls of a six-sided die?
ÁÊÁ ˜ˆ˜ ÁÊ 1 ˜ˆ k ÁÊ 5 ˜ˆ 20 − k
ÁÊÁ ˜ˆ˜ ÁÊ 3 ˜ˆ k ÁÊ 3 ˜ˆ 20 − k
ÁÁ 20 ˜˜ ÁÁ ˜˜ ÁÁ ˜˜
Á 20 ˜ Á ˜ Á ˜
Á
˜
a. ÁÁ ˜˜ ÁÁÁ ˜˜˜ ÁÁÁ ˜˜˜
c. ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
Ë k ¯Ë ¯ Ë ¯
Ë k ¯Ë ¯ Ë ¯
ÊÁ ˆ˜ Ê ˆ k Ê ˆ 20 − k
ÊÁ ˆ˜ Ê ˆ 3 Ê ˆ 17
ÁÁ 20 ˜˜ ÁÁ 5 ˜˜ ÁÁ 1 ˜˜
ÁÁ 20 ˜˜ ÁÁ 1 ˜˜ ÁÁ 5 ˜˜
Á
˜
Á
˜
Á
˜
b. ÁÁÁ ˜˜˜ ÁÁÁ ˜˜˜ ÁÁÁ ˜˜˜
d. ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜ ÁÁÁÁ ˜˜˜˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
ÁÁ ˜˜ Á 6 ˜ Á 6 ˜
Ë k ¯Ë ¯ Ë ¯
Ë 3 ¯Ë ¯ Ë ¯
____ 37. A baseball player hits the ball to left field 20% of the time, to centre field 35% of the time, and to right field
45% of the time. Which of the following expressions gives the probability distribution for the number of hits to
centre field for a game in which the batter gets 5 hits?
ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ 5 ˜˜
ÁÁ 5 ˜˜
k
5−k
k
5−k
Á
˜
c. ÁÁÁÁ ˜˜˜˜ (0.35) (0.65)
a. ÁÁÁ ˜˜˜ (0.2) (0.8)
ÁÁ ˜˜
ÁÁ ˜˜
Ëk ¯
Ëk ¯
ÊÁ ˆ˜
ÊÁ ˆ˜
ÁÁ 5 ˜˜
ÁÁ 5 ˜˜
k
5−k
k
5−k
Á
˜
b. ÁÁÁ ˜˜˜ (0.65) (0.35)
d. ÁÁÁÁ ˜˜˜˜ (0.45) (0.55)
ÁÁ ˜˜
ÁÁ ˜˜
Ëk ¯
Ëk ¯
____ 38. The probability of a computer memory chip being defective is 0.02. Which of the following statements is true?
a. In a shipment of 100 chips, two will be defective.
b. The expected number of defective chips in a shipment of 500 is ten.
c. In a shipment of 1000 chips, it is certain that at least one will be defective.
d. All statements above are false.
____ 39. A young couple plans to have a family with four children. Assuming that the behaviour of their first child does
not cause them to alter their plans, what is the expected number of girls for their family?
a. 2.5
c. 2
b. 2.25
d. 1.5
7
Name: ________________________
ID: A
____ 40. The probability of success for a binomial experiment is greater than 0.5. Which is the most accurate description
of the graph of its probability distribution?
a. symmetrical
c. highest point is right of centre
b. highest point is left of centre
d. all bars have equal height
____ 41. What is the smallest p value that will give a probability of at least 0.5 that an experiment will be successful
four times in four trials?
1
a.
c. 0.9
16
b.
0.85
d.
1
4
2
____ 42. A young couple hopes to have two children. They would like the first to be a boy and the second to be a girl.
What is the probability that their first two children will arrive as described?
a. 0
c. 0.5
b. 0.25
d. 0.75
ÊÁ ˆ˜
ÁÁ 6 ˜˜
2
4
____ 43. In the expression ÁÁÁÁ ˜˜˜˜ (0.1) (0.9) , which value represents the number of failures?
ÁÁ ˜˜
Ë 2¯
a.
b.
6
2
c.
d.
4
1
____ 44. Which statement regarding the probability distribution for a binomial experiment with p = 0.5 is not true?
a. The probability of no successes must equal the probability of no failures.
b. The graph of the distribution is symmetrical.
c. The expected value of the experiment is half the number of trials.
d. The more trials that are made, the higher the probability that all trials will be successful.
____ 45. A student suggests the following expression to represent the probability of achieving four successes in seven
trials of a binomial experiment for which the probability of success is 0.3.
ÊÁ ˆ˜
ÁÁ 7 ˜˜
ÁÁ ˜˜ (0.3) 4 (0.4) 3
ÁÁ ˜˜
ÁÁ ˜˜
Ë 4¯
What error did the student make?
a. The second exponent should be a 7.
b. The probabilities for success and failure were reversed from their proper positions.
c. The probability of failure should be 0.7.
d. The first exponent should be a 7.
____ 46. For which of the following binomial experiments could the normal approximation not be applied?
a. n = 10 and p = 0.5
c. n = 100 and p = 0.4
b. n = 20 and p = 0.2
d. n = 20 and p = 0.3
8
Name: ________________________
ID: A
____ 47. What is the value of x for the normal approximation to a binomial experiment with 50 trials and a 40%
likelihood of success for any given trial?
12
a.
c. 20
d. 25
b. 22.5
____ 48. A coin is tossed five times. What is the probability of observing exactly three heads?
5
3
a.
c.
16
32
1
3
b.
d.
32
16
____ 49. A Bernoulli trial has a probability of success of 0.4. What is the smallest number of trials for which a normal
distribution can be used to approximate its probability distribution?
a. 12.5
c. 10
b. 20
d. 13
____ 50. The z-score for a particular value of X is 0.18. What is the total probability of this or any smaller value of X
occurring?
a. 42.9%
c. 96.4%
b. 57.1%
d. 3.6%
____ 51. In order to approximate the probability that X = 15 or X = 16 for a binomial distribution, what boundary values
should we choose to obtain our z-scores?
a. 15 < X < 16
c. 14.5 < X < 16.5
b. 14 < X < 17
d. none of the above
____ 52. The probability distribution for a binomial experiment with n = 10 and p = 0.4 is graphed. Which of the
following statements is least likely to be true?
a. The highest bar should be above X = 4.
b. The graph will be higher on the left than on the right.
c. The graph will be highly symmetrical.
d. The bar above X = 3 will be higher than the bar above X = 5.
____ 53. The normal approximations to two binomial experiments are compared. Both have 20 trials, but the first has p
= 0.4 and the second has p = 0.7. Which statement is not true?
a. Both binomial distributions may be approximated by a suitable normal distribution.
b. The first distribution is more symmetrical than the second.
c. The highest point for the first distribution is found above X = 8.
d. The normal approximation is a closer fit to the actual binomial distribution for the second
experiment than for the first.
____ 54. Which of the following binomial experiments has the normal approximation with the smallest standard
deviation?
a. n = 50 and p = 0.45
c. n = 40 and p = 0.55
b. n = 20 and p = 0.45
d. n = 10 and p = 0.55
9
Name: ________________________
ID: A
____ 55. The probability of a parent allowing a child to play in the sprinkler when the temperature is above 28°C is 0.8.
What is the probability that exactly 15 of 20 children will be allowed to play in their sprinklers on a day above
this temperature?
c. 0.1746
a. 0.75
b. 0.714
d. 0.315
____ 56. What is the value of the standard deviation for the normal approximation to a binomial distribution with 600
trials and a probability of success of 0.6?
a. 12
c. 6
600
b.
d. 0.24
____ 57. What is the z-score associated with observing 5 or fewer heads for 8 tosses of a fair coin?
1
3
a.
c.
2
2 2
5
11
b.
d.
8
16
____ 58. A die is rolled 12 times. Calculate the probability that a 5 appears exactly twice.
a. 0.1667
c. 0.0139
b. 0.2961
d. 0.0004
____ 59. A novice competitor in biathlon hits 80% of her targets. What is the probability that she will hit more than 45
of 50 targets attempted?
a. 19.4%
c. 2.6%
b. 80.6%
d. 97.4%
____ 60. An antibiotic is effective against a particular strain of streptococcus 70% of the time. What is the probability
that at least 70 of 100 cases will respond when treated with this antibiotic?
a. 54.4%
c. 70%
b. 45.6%
d. 49%
10
ID: A
Sample Distributions
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
B
C
B
C
D
A
B
B
A
D
B
C
C
A
D
C
B
B
A
D
C
D
A
D
B
C
B
C
C
C
C
A
D
A
A
A
C
B
1
ID: A
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
C
C
A
B
C
D
C
B
C
A
D
B
C
C
D
D
C
A
C
B
C
A
2