Question 1

A bag contains 5 red chips and 12 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are both red?

Accepted Answer

A) 0.621 
B) 0.250 
C) 0.559 
D) 0.441 
E) 0.074 
A) 0.621 
B) 0.250 
C) 0.559 
D) 0.441 
E) 0.074

Question 2

The table below describes the smoking habits of a group of asthma sufferers. $\begin{array}{r|cccc} 
&&Light &Heavy \
& \text { Nonsmoker } & \text { smoker } & \text { smoker } & \text { Total } \
\hline \text { Men } & 331 & 78 & 82 & 491 \
\text { Women } & 345 & 81 & 89 & 515 \
\text { Total } & 676 & 159 & 171 & 1006
\end{array}$ What is the probability that a woman is a nonsmoker?

Accepted Answer

A) 0.343 
B) 0.672 
C) 0.512 
D) 0.67 
E) 0.51 
A) 0.343 
B) 0.672 
C) 0.512 
D) 0.67 
E) 0.51

Question 3

You are dealt a hand of three cards,one at a time.Find the probability that you have at least one queen.

Accepted Answer

A) 0.217 
B) 0.204 
C) 0.068 
D) 0.783 
E) 0.213 
A) 0.217 
B) 0.204 
C) 0.068 
D) 0.783 
E) 0.213

Question 4

A box contains 16 batteries of which 6 are still working.Anne starts picking batteries one at a time from the box and testing them.Find the probability that she has to pick 5 batteries in order to find one that works.

Accepted Answer

A) 0.007 
B) 0.058 
C) 0.001 
D) 12.360 
E) 0.029 
A) 0.007 
B) 0.058 
C) 0.001 
D) 12.360 
E) 0.029

Question 5

In filling out a ballot for your local M.P.,the events of voting for the Conservative candidate and voting for the Liberal candidate

Accepted Answer

A) Disjoint 
B) Independent 
C) Neither 
D) Both 
A) Disjoint 
B) Independent 
C) Neither 
D) Both

Question 6

Suppose that the Canadian Red Cross says that about 45% of the Canadian population has Type O blood,40% Type A,11% Type B,and the rest Type AB.Among six donors,what is the probability that no one is Type A?

Accepted Answer

A) 0.047 
B) 2.400 
C) 0.004 
D) 3.600 
E) 0.036 
A) 0.047 
B) 2.400 
C) 0.004 
D) 3.600 
E) 0.036

Question 7

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all diamonds.

Accepted Answer

A) 0.013 
B) 0.231 
C) 0.016 
D) 0.750 
E) 0.705 
A) 0.013 
B) 0.231 
C) 0.016 
D) 0.750 
E) 0.705

Question 8

A study conducted at a college shows that 70% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that 7 randomly selected graduates all find jobs in their chosen field within a year of graduating.

Accepted Answer

A) 0.1000 
B) 0.4900 
C) 4.9000 
D) 0.9176 
E) 0.0824 
A) 0.1000 
B) 0.4900 
C) 4.9000 
D) 0.9176 
E) 0.0824

Question 9

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all aces.Round your answer to five decimal places.

Accepted Answer

A) 0.00018 
B) 0.01294 
C) 0.00046 
D) 0.17575 
E) 0.00025 
A) 0.00018 
B) 0.01294 
C) 0.00046 
D) 0.17575 
E) 0.00025

Question 10

A high school offers these statistics: 59% of incoming students come from single-parent homes.
41% of incoming students come from two-parent homes.
21% of incoming students from single-parent homes eventually go on to get a college education.
44% of incoming students from two-parent homes eventually go on to get a college education.
What percent of students who get a college education come from single-parent families?

Accepted Answer

A) 59% 
B) 21% 
C) 59.3% 
D) 68.7% 
E) 40.7% 
A) 59% 
B) 21% 
C) 59.3% 
D) 68.7% 
E) 40.7%

Question 11

A high school offers these statistics: 27% of incoming students come from single-parent homes.
45% of incoming students come from single-parent homes eventually go on to get a college education.
59% of incoming students from two-parent homes eventually go on to get a college education.
Is there any evidence that an incoming student's chances to eventually get a college education depend on whether they come from a single parent or two parent home? Explain.

Accepted Answer

A) No,the probability of going on to get a college education does not depend on whether the student comes from a single-parent or a two-parent home. 
B) Yes, P(single-parent home and college education)= (0.27)∙ (0.45);
P(two-parent home and college education)= (0.73)∙ (0.59).
These are not equal. 
C) Yes,the probability of going on to get a college education depends on whether the student comes from a single-parent or two-parent home. For students from single-parent homes,45% go on to get a college education.
For students from two-parent homes,59% go on to get a college education. 
D) No,because P(single-parent home and college education)= P(single-parent home)∙ P(college education). 
E) No,it is possible for both things to happen. P(single-parent home and college education)= (0.27)∙ (0.45).This is greater than zero. 
A) No,the probability of going on to get a college education does not depend on whether the student comes from a single-parent or a two-parent home. 
B) Yes, P(single-parent home and college education)= (0.27)∙ (0.45);
P(two-parent home and college education)= (0.73)∙ (0.59).
These are not equal. 
C) Yes,the probability of going on to get a college education depends on whether the student comes from a single-parent or two-parent home. For students from single-parent homes,45% go on to get a college education.
For students from two-parent homes,59% go on to get a college education. 
D) No,because P(single-parent home and college education)= P(single-parent home)∙ P(college education). 
E) No,it is possible for both things to happen. P(single-parent home and college education)= (0.27)∙ (0.45).This is greater than zero.

Question 12

A bag contains 10 red chips and 9 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are the same color?

Accepted Answer

A) 0.529 
B) 0.474 
C) 0.526 
D) 0.500 
E) 0.263 
A) 0.529 
B) 0.474 
C) 0.526 
D) 0.500 
E) 0.263

Question 13

You roll a fair die four times.What is the probability that the numbers you roll are not all 6's?

Accepted Answer

A) 0.999 
B) 0.0008 
C) 0.833 
D) 0.518 
E) 0.482 
A) 0.999 
B) 0.0008 
C) 0.833 
D) 0.518 
E) 0.482

Question 14

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a diamond given that it is a queen.

Accepted Answer

A) 0.000 
B) 0.500 
C) 0.077 
D) 0.250 
E) 0.333 
A) 0.000 
B) 0.500 
C) 0.077 
D) 0.250 
E) 0.333

Question 15

You are dealt a hand of three cards,one at a time.Find the probability that you get no kings.

Accepted Answer

A) 0.315 
B) 0.783 
C) 0.787 
D) 0.414 
E) 0.118 
A) 0.315 
B) 0.783 
C) 0.787 
D) 0.414 
E) 0.118

Question 16

In one town in British Columbia,only 24% of days are sunny.A company's records indicate that on sunny days 1.8% of employees will call in sick.When it is not sunny,0.9% of employees will call in sick.What percent of employees call in sick on a randomly selected day?

Accepted Answer

A) 1.8% 
B) 0.684% 
C) 0.432% 
D) 1.116% 
E) 1.35% 
A) 1.8% 
B) 0.684% 
C) 0.432% 
D) 1.116% 
E) 1.35%

Question 17

63% of students at one college drink coffee,and 16% of people who drink coffee suffer from insomnia.What is the probability that a randomly selected student drinks coffee and suffers from insomnia?

Accepted Answer

A) 0.1008 
B) 0.6892 
C) 0.5292 
D) 0.79 
E) 0.16 
A) 0.1008 
B) 0.6892 
C) 0.5292 
D) 0.79 
E) 0.16

Question 18

Shameel has a flight to catch on Monday morning.His father will give him a ride to the airport.If it rains,the traffic will be bad and the probability that he will miss his flight is 0.04.If it doesn't rain,the probability that he will miss his flight is 0.03.The probability that it will rain on Monday is 0.28.What is the probability that Shameel misses his flight?

Accepted Answer

A) 0.0328 
B) 0.0216 
C) 0.035 
D) 0.0112 
E) 0.04 
A) 0.0328 
B) 0.0216 
C) 0.035 
D) 0.0112 
E) 0.04

Question 19

The sales bin in a clothing store contains an assortment of t-shirts in different sizes.There are 4 small,7 medium,and 9 large shirts.Alan is looking for a large shirt.He starts grabbing shirts one at a time and checking the size.After he checks each shirt,he leaves it outside the bin.What is the probability that the first large shirt he finds is the third one he checks?

Accepted Answer

A) 0.074 
B) 0.136 
C) 0.145 
D) 0.124 
E) 0.091 
A) 0.074 
B) 0.136 
C) 0.145 
D) 0.124 
E) 0.091

Question 20

An online poll asked people how likely they were to see a new movie that was coming out in the summer.Here's how they responded: $$\begin{array} { l | l } 
\text { Response } & \text { Number } \
\hline \text { Will definitely see it } & 223 \
\text { Will probably see it } & 251 \
\text { Will probably not see it } & 330 \
\text { Will definitely not see it } & 385 \
\hline \text { Total } & 1189
\end{array}$$ Let's call someone who responded that they would definitely or probably see it a "likely viewer" and the other two categories,"unlikely viewer." If we select two people at random from this sample,what is the probability that one is a likely viewer and one isn't?

Accepted Answer

A) 0.159 
B) 0.305 
C) 0.240 
D) 0.152 
E) 0.479 
A) 0.159 
B) 0.305 
C) 0.240 
D) 0.152 
E) 0.479

Exam 13: Probability Rules

A bag contains 5 red chips and 12 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are both red?

The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men 331 78 82 491 Women 345 81 89 515 Total 676 159 171 1006 What is the probability that a woman is a nonsmoker?

You are dealt a hand of three cards,one at a time.Find the probability that you have at least one queen.

A box contains 16 batteries of which 6 are still working.Anne starts picking batteries one at a time from the box and testing them.Find the probability that she has to pick 5 batteries in order to find one that works.

In filling out a ballot for your local M.P.,the events of voting for the Conservative candidate and voting for the Liberal candidate

Suppose that the Canadian Red Cross says that about 45% of the Canadian population has Type O blood,40% Type A,11% Type B,and the rest Type AB.Among six donors,what is the probability that no one is Type A?

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all diamonds.

A study conducted at a college shows that 70% of the school's graduates find a job in their chosen field within a year after graduation.Find the probability that 7 randomly selected graduates all find jobs in their chosen field within a year of graduating.

You are dealt a hand of three cards,one at a time.Find the probability that your cards are all aces.Round your answer to five decimal places.

A bag contains 10 red chips and 9 blue chips.Two chips are selected randomly without replacement from the bag.What is the probability that the two chips are the same color?

You roll a fair die four times.What is the probability that the numbers you roll are not all 6's?

You draw a card at random from a standard deck of 52 cards.Find the probability that the card is a diamond given that it is a queen.

You are dealt a hand of three cards,one at a time.Find the probability that you get no kings.

In one town in British Columbia,only 24% of days are sunny.A company's records indicate that on sunny days 1.8% of employees will call in sick.When it is not sunny,0.9% of employees will call in sick.What percent of employees call in sick on a randomly selected day?

63% of students at one college drink coffee,and 16% of people who drink coffee suffer from insomnia.What is the probability that a randomly selected student drinks coffee and suffers from insomnia?

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