Question 1

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that both items are not defective?
A) 0.3750
B) 0.3846
C) 0.1500
D) 0.6154
E) 0.2000

Accepted Answer

= .375

Question 2

A machine is made up of 3 components: an upper part, a middle part, and a lower part. The machine is then assembled. 5 percent of the upper parts are defective, 4 percent of the middle parts are defective, and 1 percent of the lower parts are defective. What is the probability that a machine is not defective?
A) 0.1000
B) 0.9029
C) 0.8000
D) 0.0002
E) 0.7209

Accepted Answer

(.95)(.96)(.99) = .9029

Question 3

A card is drawn from a standard deck. What is the probability the card is an ace, given that it is a club?
A) 1/52
B) 1/13
C) 4/13
D) 1/4

Accepted Answer

Set up sample space: 52 cards; 13 are clubs, one of which is an ace.

Question 4

A group has 12 men and 4 women. If 3 people are selected at random from the group, what is the probability that they are all men?
A) 0.4219
B) 0.5143
C) 0.3929
D) 0.0156
E) 0.0045

Accepted Answer

= .392857

Question 5

A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the two faces is 9?
A) 1/3
B) 1/36
C) 1/6
D) 1/2
E) 1/4

Accepted Answer

Set up sample spaces: 36 total; 4 total to 9; 2 of these have a three on the face. Given that there are 4 choices and 2 have a three, the probability is ½.

Question 6

A coin is tossed 6 times. What is the probability that at least one head occurs?
A) 63/64
B) 1/64
C) 1/36
D) 5/6
E) 1/2

Accepted Answer

(1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = P(No Heads) = 1/64
1 - 1/64 = 63/64

Question 7

A card is drawn from a standard deck. Given that a face card is drawn, what is the probability it will be a king?
A) 1/3
B) 1/13
C) 4/13
D) 1/12
E) 1/4

Accepted Answer

(4 kings)/(12 face cards)

Question 8

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that the item from Container 1 is defective and the item from Container 2 is not defective?
A) 0.3846
B) 0.2250
C) 0.3750
D) 0.6154
E) 0.1500

Accepted Answer

= .225

Question 9

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table.  If a student is male, what is the probability he is a C student?
A) 0.05
B) 0.10
C) 0.30
D) 0.17
E) 0.50

Accepted Answer

P(C | Male) == .1667

Question 10

What is the probability of winning four games in a row, if the probability of winning each game individually is 1/2?
A) 1/4
B) 1/8
C) 1/2
D) 3/16
E) 1/16

Accepted Answer

=

Question 11

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table.  What is the probability that a student is female and a C student?
A) .45
B) .50
C) .70
D) .25
E) .05

Accepted Answer

Read off contingency table = P(F ∩ C) = .45

Question 12

Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?
A) 0.115
B) 0.500
C) 0.231
D) 0.462
E) 0.308

Accepted Answer

P(Red | Face) ===

Question 13

Given the standard deck of cards, what is the probability of drawing a red card, given that it is a face card?
A) 0.500
B) 0.115
C) 0.231
D) 0.077
E) 0.308

Accepted Answer

P(Red | Face) === .5

Question 14

A machine is produced by a sequence of operations. On average, one out of every 1000 machines produced is defective. What is the probability that two machines selected at random are both nondefective?
A) 0.000999
B) 0.001
C) 0.002
D) 0.998
E) 0.500

Accepted Answer

(.999)(.999) = .998

Question 15

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective?
A) 0.2250
B) 0.6250
C) 0.2500
D) 0.4750
E) 0.1500

Accepted Answer

Container 1 P(Defective) = 3/8 = .375; Container 2 P(Defective) = 2/5 = .400
P(Both defective) = .375 × .400 = .150; P(Neither defective) = (1 - .375) × (1 - .40) = .375
P(Only one defective) = 1 - (.150 + .375) = .475

Question 16

A family has two children. What is the probability that both are girls, given that at least one is a girl?
A) 1/8
B) 1/4
C) 1/2
D) 1/3
E) 1/6

Accepted Answer

Set up sample space: 3 possible for the given statement BG, GB and GG; 2 of these have at least one girl; 1 has two girls so the probability that GG is 1 out of 3 or 1/3.

Question 17

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Construct a contingency table.

Accepted Answer

The answer of At a college, 70 percent of the...

Question 18

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table.  What is the probability that a student is male and not a C student?
A) .45
B) .50
C) .70
D) .25
E) .05

Accepted Answer

Read off contingency table: P(M ∩ not C) = .25

Question 19

A person is dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs?
A) 0.2500
B) 0.0962
C) 0.0769
D) 0.0010
E) 0.0005

Accepted Answer

= 0.0004951

Question 20

Independently, a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the probability of observing a head on the coin, an ace on the card, and a five on the die?
A) 0.0064
B) 0.1000
C) 0.7436
D) 0.0096
E) 0.5000

Accepted Answer

1/2 × 4/52 × 1/6 = 1/156 = 0.0064

Quiz 4: Probability and Probability Models

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that both items are not defective?

A card is drawn from a standard deck. What is the probability the card is an ace, given that it is a club?

A group has 12 men and 4 women. If 3 people are selected at random from the group, what is the probability that they are all men?

A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the two faces is 9?

A coin is tossed 6 times. What is the probability that at least one head occurs?

A card is drawn from a standard deck. Given that a face card is drawn, what is the probability it will be a king?

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that the item from Container 1 is defective and the item from Container 2 is not defective?

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student is male, what is the probability he is a C student?

What is the probability of winning four games in a row, if the probability of winning each game individually is 1/2?

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is female and a C student?

Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?

Given the standard deck of cards, what is the probability of drawing a red card, given that it is a face card?

A machine is produced by a sequence of operations. On average, one out of every 1000 machines produced is defective. What is the probability that two machines selected at random are both nondefective?

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective?

A family has two children. What is the probability that both are girls, given that at least one is a girl?

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Construct a contingency table.

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is male and not a C student?

A person is dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs?

Independently, a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the probability of observing a head on the coin, an ace on the card, and a five on the die?