Q: Are the events “being a student” and “oppose the proposed ban” independent? Use the survey data to justify your answer.

No, because $$ P( ext{student} ext{ and } ext{oppose}) \neq P( ext{student}) \times P( ext{oppose}) $$

Q: The owner of Jobs-for-All claims a 90% chance of finding full-time employment after graduation. What is the probability that all three randomly selected graduates found full-time jobs?

$$ 0.9 \times 0.9 \times 0.9 = 0.729 $$

Q: In the Jobs-for-All scenario, what is the probability that none of the three graduates found full-time jobs?

$$ 0.1 \times 0.1 \times 0.1 = 0.001 $$

Q: What is the probability that at least one of the three graduates found full-time work, given the Jobs-for-All claim?

$$ 1 - (0.1 \times 0.1 \times 0.1) = 0.999 $$

Q: Twenty curling teams compete for gold, silver, and bronze medals. In how many different ways can the medals be awarded?

$$ 20 \times 19 \times 18 = 6840 $$

Question 1

A survey at a Canadian university asked 5000 faculty and students whether they support a proposed ban on junk food. If one individual is selected at random, what is the probability that the individual opposes the proposed ban?

Accepted Answer

$$ \frac{3540}{5000} = 0.7080 $$

Question 2

In the university survey, what is the probability that the individual selected is a student?

Accepted Answer

$$ \frac{4700}{5000} = 0.9400 $$

Question 3

What is the probability that the individual selected is a student and opposes the proposed ban?

Accepted Answer

$$ \frac{3500}{5000} = 0.7000 $$

Question 4

Are the events “being a student” and “support the proposed ban” mutually exclusive?

Accepted Answer

No, because some students support the proposed ban.

Question 5

Are the events “being a student” and “oppose the proposed ban” independent? Use the survey data to justify your answer.

Accepted Answer

No, because $$ P(	ext{student} 	ext{ and } 	ext{oppose}) 
eq P(	ext{student}) 	imes P(	ext{oppose}) $$

Question 6

A men’s wear retail outlet sold 200 dress shirts: 15 small, 70 medium, 85 large, and 30 extra large. What is the probability that the next customer will buy a large dress shirt?

Accepted Answer

$$ \frac{85}{200} = 0.4250 $$

Question 7

What type of probability is used to determine the probability that the next customer will buy a large dress shirt?

Accepted Answer

Empirical probability, because it is based on observed frequencies.

Question 8

The owner of Jobs-for-All claims a 90% chance of finding full-time employment after graduation. What is the probability that all three randomly selected graduates found full-time jobs?

Accepted Answer

$$ 0.9 	imes 0.9 	imes 0.9 = 0.729 $$

Question 9

In the Jobs-for-All scenario, what is the probability that none of the three graduates found full-time jobs?

Accepted Answer

$$ 0.1 	imes 0.1 	imes 0.1 = 0.001 $$

Question 10

What is the probability that at least one of the three graduates found full-time work, given the Jobs-for-All claim?

Accepted Answer

$$ 1 - (0.1 	imes 0.1 	imes 0.1) = 0.999 $$

Question 11

Twenty curling teams compete for gold, silver, and bronze medals. In how many different ways can the medals be awarded?

Accepted Answer

$$ 20 	imes 19 	imes 18 = 6840 $$

Question 12

In a lottery, you must select 3 numbers (in any order) out of 25 to win the top prize. What is the probability of winning with one ticket?

Accepted Answer

$$ \frac{1}{\binom{25}{3}} = \frac{1}{2300} = 0.000435 $$

Question 13

Major Motors sells new and used cars. 60% of sales are new cars, and 50% of new car buyers purchase an extended warranty. What is the probability that a new customer will purchase a new car and an extended warranty?

Accepted Answer

$$ 0.6 	imes 0.5 = 0.3 $$

Question 14

What is the probability that a new customer at Major Motors will purchase an extended warranty?

Accepted Answer

$$ (0.6 	imes 0.5) + (0.4 	imes 0.75) = 0.3 + 0.3 = 0.6 $$

Question 15

Are the events 'buys a new car' and 'purchases an extended warranty' independent at Major Motors?

Accepted Answer

No, because $$ P(	ext{extended warranty} | 	ext{new car}) 
eq P(	ext{extended warranty}) $$

Question 16

When two dice are tossed, what is the theoretical probability that their sum is at least 8?

Accepted Answer

$$ \frac{15}{36} = 0.4167 $$

Question 17

In the Sun Exposure Survey, if 4,022 Canadians responded, and 200 had red hair, what is the probability that a randomly selected respondent has red hair?

Accepted Answer

$$ \frac{200}{4022} = 0.0497 $$

Question 18

In the Sun Exposure Survey, suppose 100 respondents had blonde hair and were diagnosed with precancer, and 500 respondents had blonde hair. What is the probability that a randomly selected respondent with precancer has blonde hair?

Accepted Answer

$$ \frac{100}{500} = 0.2 $$

Step-by-Step Guidance for Assignment 2: Probability and Statistics Problems

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드