Download 1. Which pair has equally likely outcomes? List the letters of the two

1. Which pair has equally likely outcomes? List the letters of the two choices below which have equal
probabilities of success, separated by a comma. A standard deck of cards has 12 face cards and four
Aces (Aces are not face cards).
A. rolling a sum of 9 on two fair six sided dice
B. drawing the Queen of Diamonds out of a standard 52 card deck given it’s a face card.
C. rolling a sum of 11 on two fair six sided dice
D. drawing a king out of a standard 52 card deck given it’s a face card.
E. rolling a sum of 10 on two fair six sided dice
(Points : 3)
a. rolling a sum of 9 on two fair six sided dice "
There are 36 (6^2) possible outcomes.
(3,6)
(4,5)
(5,4)
(6,3)
Four of them sum to 9.
P(A given B) = P(A|B) = P(A and B)/P(B)
P(9)= 4/36 = 1/9
Correct
b. Drawing the Queen of diamonds out of a standard 52 card deck given it’s a face card"
There are 12 face cards.
There is 1 Queen of Diamonds.
P(QD,F)= 1/12
Correct
c. Rolling a sum of 11 on two fair six sided dice.
(5,6)
(6,5)
P(11)=2/36 = 1/18
Correct
d. Drawing a king out of a standard 52 card deck given it’s a face card.
There are 12 face cards.
There are 4 Kings.
P(k,F)=4/12=1/3
Correct
e. Rolling a sum of 10 on two fair six sided dice.
(4,6)
(5,5)
(6,4)
P(10)=3/36=1/12
Correct
f.No two pairs match in their probabilities.
Answer: B,E
2. A mini license plate for a toy car must consist of a two numbers followed by a vowel. Each number
must be a 3 or a 6. Repetition of digits is permitted.
• Use the counting principle to determine the number of points in the sample space.
• Construct a tree diagram to represent this situation and submit it to the W5: Assignment 2 Dropbox
( need help)
• List the sample space.
• Determine the exact probability of creating a mini license plate with a 3. Give solution exactly in
reduced fraction form.
Ans:
•Use the counting principle to determine the number of points in the sample space.
pick a vowel: 5 ways
pick a number: 2 ways
pick a number: 2 ways
===
# of points in the sample space = 5*2*2 = 20
Correct
-----•Construct a tree diagram to represent this situation and submit it to the
•List the sample space.
a33,a37,a73,a77
Same pattern with e,i,o,u
Incorrect since the numbers come first.
33a, 33e, 33i, 33o, 33u, 36a, 36e, 36i, 36o, 36u, 66a, 66e, 66i, 66o, 66u, 63a, 63e, 63i, 63o, 63u
----------------------------------•Determine the exact probability of creating a mini license plate with an A.
Give solution exactly in reduced fraction form.
Ans: 4/20 = 1/5
Correct, but the question is different than the question further above.
Determine the exact probability of creating a mini license plate with a 3. Give solution exactly in
reduced fraction form.
15/20 = 3/4
(Points : 12)
3. Given that P(A) = 0.7 and P(B) = 0.2, and P(A and B) = 0.14, determine P(B|A). (Points : 3)
0.90
0.70
0.50
0.20
P(B|A) = [P(A and B)/P(A)] = 0.14/0.70 = .20
Correct
4. An identification code is to consist of two letters followed by six digits. How many different codes
are possible if repetition is permitted? (Points : 2)
Code: LLDDDDDD
There are 26 letters
There are 10 digits
# of codes = 26^2*10^6 = 676,000,000
Correct
5. Show all work. A disc jockey has 7 songs to play. Three are slow songs, and four are fast songs.
Each song is to be played only once. In how many ways can the disc jockey play the 7 songs if
• The songs can be played in any order.
• The first song must be a slow song and the last song must be a slow song.
• The first two songs must be fast songs.
(Points : 3)
In how many ways can the disc jockey play the 7 songs if
the songs can be played in any order:::7! = 5040 ways
Correct
------------------------------------------------------------------• The first song must be a slow song and the last song must be a slow song.
1st song: 3 ways
last song: 2 ways
Middle 5 songs: 5! = 120 ways
Total ways: 3*2*120 =720 ways
Correct
-----------------------------------• The first two songs must be fast songs.
1st song: 4 ways
2nd song: 3 ways
last 5 songs: 5! = 120
Total ways:4*3*120 = 1440 ways
Correct
==================================
6. Evaluate 10C8 (Points : 2)
45
90
40320
2
10C8 is the same as 10C2
10C2 = [10*9]/[1*2] = 45
Correct
======================
7. Show all work. Mary purchased a package of 20 different plants, but she only needed 16 plants for
planting. In how many ways can she select the 20 plants from the package to be planted? (Points : 3)
Note: # of ways of selecting 16 is the
same as # of ways of not selecting 4.
20C16 = 20C4 = (20*19*18*17)/(1*2*3*4) = 4845
Correct
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==============
8. Each of the numbers 0 through 24 is written on a piece of paper and all of the pieces of paper are
placed in a hat. One number is selected at random. Determine the probability that the number
selected is even. Note: 0 is considered an even number.
(Points : 2)
13/25
13/24
11/24
1/2
Even digits: 0,2,4,6,8,10,12,14,16,18,20,22,24
P(even digit) = 13/25
Correct
9. Consider the Venn diagram below. The numbers in the regions of the circle
indicate the number of items that belong to that region.
Determine
• n(A)
• n(B)
• P(A)
• P(B)
• P(A|B)
• P(B|A)
Answer:
n(A) = 30+20 = 50
n(B) = 90+20 = 110
P(A) = 50/160
P(B) = 110/160
P(A|B)= 20/110
P(B|A)= 20/50
If there are no numbers outside of both A and B:
P(A) = 50/140 = 5/14
P(B) = 110/140 = 11/14
The rest are correct
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=====================
1. A bag contains 8 pink marbles, 5 green marbles and 10 brown marbles. What is the chance of
drawing a brown marble? If a brown marble is drawn then placed back into the bag, and a second
marble is drawn, what is the probability of drawing a pink marble? Give solutions exactly in reduced
fraction form, separated by a comma.
(Points : 3)
Ans:
(10/23),(8/23)
Correct
==================== =====================================
2. A mini license plate for a toy car must consist of two letters followed by a one digit odd number.
Each letter must be a K or a Q. Repetition of letters is not permitted.
• Use the counting principle to determine the number of points in the sample space.
• Construct a tree diagram and submit it to the W5: Assignment 3 Dropbox.
• List the sample space.
• Determine the exact probability of creating a mini license plate with a 3. Give solution exactly in
reduced fraction form.
(Points : 12)
1. Use the counting principle to determine the number of points in the sample space.
# of points = 2*1*3 = 6
Incorrect since you seem to have neglected 1 and 9
2 x 5 = 10
----------------------------------2. Construct a tree diagram
------3. List the sample space.
KQ3,kQ5,KQ7,QK3,QK5,QK7
Incorrect
KQ1, KQ3, KQ5, KQ7, KQ9, QK1, QK3, QK5, QK7, QK9
---------------4. Determine the exact probability of creating a
mini license plate with a 3.
2/6=1/3
Incorrect
2/10
===================
2. A parent can choose from 5 types of protein, 6 vegetables and 4 desserts. If the parent serves a
meal of 1 protein, 1 vegetable and 1 dessert to the family, how many different meals can be served?
(Points : 2)
Ans: 5*6*4 = 120 different means
Correct except for the “n,” in meals
Your answers are so good I have to search for mistakes
=======================================================
3. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face
cards and four Aces (Aces are not face cards). Find the probability of selecting
•an odd prime number under 10 given the card is a club. (1 is not prime.)
P(3,5,7|♣)
= 3/12 = 1/4
•a Jack, given that the card is not a heart.
P(J|♠♣♦)
= 3/39 = 1/13
•a King given the card is not a face card.
0 since a king is a face card
Show step by step work. Give all solutions exactly in reduced fraction form.
(Points : 3)
5. In how many ways can 8 instructors be assigned to six sections of a course in mathematics?
(Points : 2)
Let the sections select the instructors:
8C6 = 8C2 = (8*7)/(1*2) = 28 ways
Incorrect since the order would matter.
8P6 = 8!/2! = 20,160
6. In how many different ways can the top eight new indie bands be ranked on a top eight list? The
top hit song for each of the eight bands will compete to receive monetary awards of $1000, $500,
$250 and $100, respectively. In how many ways can the awards be given out?
(Points : 3)
i. Ans: 8! = 40320
Correct
ii. 1st prize 8 ways
2nd prize 7 ways
3rd prize 6 ways
4th prize 5 ways
Ans: 8P4 = 8!/(8-4)! = 8*7*6*5 = 1680
Correct
7. A bag contains a total of 9 batteries, of which five are defective. Selecting two at random, without
replacement, determine the probability that none of the batteries you select are good.
(Points : 2)
5/18
5/9
2/9
20/81
Combination=nCr=n!/((n-r)!*r!)
P=5C2/9C2
=10/36
= 5/18 the probability that none of the batteries you select are good.
Correct
4 are not defective.
P(2 good) = 4C2/9C2 = 8/36
=2/9
The probability that both are good is 1/6 (4C2 = 6, not 8).
8. Evaluate: 7C5
(Points : 3)
21
35
12
42
7C5 = 18C8 = [7*6]=42
Incorrect
7C5 = 7 x 6 / 2 = 21
9.
Given that P(A) = 0.4, P(B) = 0.8, and P(A and B) = 0.40, determine P(A|B)
(Points : 3)
0.67
0.80
0.50
0.75
P(A|B) = P(A and B)/P(B) = 0.4/0.80 = 1/2 = 0.5
Correct
10. If P(A or B) = 0.8, P(A) = 0.1 and P(B) = 0.9, determine
P(A and B).
(Points : 3)
0.90
0.20
0.80
0.08
P(A or B)= P(A) + P(B) - P(A and B)
0.8=0.1+0.9-x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the
equation.
0.1+0.9-x=0.8
Add 0.9 to 0.1 to get 1.
1-x=0.8
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by
subtracting 1 from both sides.
-x=-1+0.8
Add 0.8 to -1 to get -0.2.
-x=-0.2
Multiply each term in the equation by -1.
-x*-1=-0.2*-1
Multiply -x by -1 to get x.
x=-0.2*-1
Multiply -0.2 by -1 to get 0.2.
x=0.2
Correct, but unnecessarily complex.
P(A and B)= P(A) + P(B) - P(A or B) = 0.1 + 0.9 – 0.8 = 0.2
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