Download Applications of Math 12

Applications of Math 12 - Probability Review
1. A regular 6-sided die is rolled 50 times. The number 6 appears 10 times.
a. What is the experimental probability of rolling a 6?
b. What is the theoretical probability of rolling a 6?
2. One card is drawn from a standard deck of 52 playing cards. Determine probability of drawing
a. A black king.
b. An even numbered red card. (Face cards do not count as numbered cards.)
c. An ace.
3. In a raffle, 300 tickets are sold. Determine the probability of winning the raffle if you purchase
a. 1 ticket
b. 20 tickets
4. A pinball game has pins arranged as shown below.
a. Determine the number of different pathways to each exit.
b. Determine the total number of different pathways through the pins.
c. What is the theoretical probability for exiting at E?
d. What is the theoretical probability for exiting at B?
5. For each of the diagrams below, determine the number of different pathways
to exit X if you start at A and move either left or down on each move.
6. Write the sample space for the following experiments and determine the probability of the required
event:
a. a coin is tossed and one six-sided die is rolled at the same time P(H and 5) P(H and 4 or 2)
b. a family has two children.
P(1 boy and 1 girl)
P(both the same gender)
c. a pair of dice is rolled
P(a sum of 6)
P(doubles)
7. Eleven cards are printed, each containing one of the letters used to spell the word PROBABILITY. If a
card is picked at random, what is the probability that it is a B?
8. How many different 3-digit odd numbers are possible if repeated digits are allowed?
9. How many 5-digit numbers are there if repeated digits are not allowed?
10. Seven books are to be placed in line on a shelf. In how many different ways can these books be
arranged?
11. Charlie, Davie, Eddie, and Freddie are lined up to buy their lunch. In how many different ways can
they arrange themselves in line?
12. Five girls and 4 boys are lined up to buy dance tickets. In how many different ways can they line up if
the girls must occupy the first five positions in the line?
13. Which of the following events are independent?
a. rolling a six on a die and obtaining tails on a coin.
b. rolling an odd number on one die and rolling an even number on another die.
c. a mother has blonde hair, and her child has blonde hair.
d. the first card dealt is a spade, the second card is a spade (without replacement).
e. selecting one tulip from a vase and one tulip from another vase
14. Which of the following events are mutually exclusive?
a. rolling an even number or rolling a prime number.
b. selecting a gift that is edible or a gift that is a CD.
c. Choosing a card that is a spade or a card that is a face card.
d. your hockey team scores a goal or your team wins the game.
15. A letter is picked at random from the alphabet. Find the probability that the letter is contained in the
word phone or in the word house.
16. A ball is drawn at random from a bag containing 3 white, 2 red, and 5 blue balls. What is the
probability of getting a red or blue ball?
17. The probabilities that Rocky and James will be elected as the chairperson are
1
2
and
4
7
respectively. Find the probability that neither of them will be elected.
18. Find the probability of getting a sum of 7 on the first throw of two dice and a sum of 4 on the second
throw.
19. A bag contains 5 red, 3 white, and 2 blue marbles. If 2 marbles are selected in succession, what is
the probability of drawing:
With replacement:
a. 1 red and then 1 white
b. the same colors
Without replacement: c. 2 red marbles
d. 1 red and then 1 blue
20. Fifty tickets, numbered consecutively 1 to 50, are placed in a box. What is the probability that in 3
separate drawings, the following selections occur?
a. 3 odd numbers, if replacement occurs
b. 3 odd numbers if no replacement occurs
21. A red and a green die are thrown. What is the probability that each of the following occurs?
a. neither shows a 2
b. both show different numbers.
22. A lock on a briefcase has 3 wheels, each labeled from 0 to 9. How many codes are possible if
a. there are no repeated digits in the code
b. the code may have repeated digits
23. A collection of 15 transistors contains 3 that are defective. If 2 transistors are selected in succession without
replacement, what is the probability that:
a. 1 is defective and 1 is non-defective
b. at least 1 of them is defective (Think one defective or two defective)
24. A bag contains 7 red and 4 white marbles. Three balls are selected without replacement. What is the
probability that the following occurs?
a. all the same color
b. at least 1 white
25. Consider two events such that P(A) = 0.3, P(B) = 0.4, and P(A & B) = 0.18. Comment on whether the events
A and B are independent.
KEY
1a. 1/5
b. 1/6
2a. 1/26
b. 5/26
c. 1/13
3a. 1/300
b. 1/15
4a. A = 1 B = 6 C = 15
D = 20 E = 15 F = 6 G = 1
b. 64
c. 15/64
d. 3/32
5a. 20
b. 35
c. 400
6a, 1/12, 1/6
b. 1/2, 1/2
c. 5/36, 1/6
7. 2/11
8. 360
9. 27216
10. 5040
11. 24
12. 2880
13. a, b, e
14. a, b
15. 4/12
16. 7/10
17. 15/28
18. 1/72
19a. 3/20
b. 19/50
c. 2/9
d. 1/9
20a. 1/8
b. 23/196
21. 25/36
b. 5/6
22a. 720
b. 1000
23a. 6/35
b. 1/5
24a. 27/55
b. 4/11
25. P(A)  P(B) = P(A & B) if they’re
independent. Since P(A)  P(B)  P(A &
B), A and B must be dependent events.