Probability in Business: Master Chance and Likelihood

Question 1

A lottery has a 1 in 100,000 chance of winning. What is the probability of not winning?

Accepted Answer

99,999/100,000

Answer

1/100,000

Answer

100,000/1

Answer

0

Question 2

A box contains 10 items, of which 4 are defective. What is the probability of selecting 2 defective items without replacement?

Accepted Answer

4/45

Answer

3/10

Answer

4/10

Answer

1/10

Question 3

A company estimates that the probability of a customer returning a product is 10%. If 100 customers purchase a product, what is the probability that at least one customer will return it?

Accepted Answer

1 - (0.9)^100

Answer

100/10

Answer

1/10

Answer

(0.9)^100

Question 4

A company has three machines, A, B, and C, which produce 60%, 20%, and 20% of the total output, respectively. What is the probability that a randomly selected unit is produced by machine A?

Accepted Answer

0.6

Answer

0.5

Answer

0.3

Answer

0.4

Question 5

A bag contains 5 red balls and 3 blue balls. If two balls are drawn from the bag without replacement, what is the probability that both balls are red?

Accepted Answer

5/14

Answer

1/14

Answer

1/28

Answer

5/28

Question 6

A company estimates that the probability of a customer making a purchase is 0.4. If 100 customers visit the store, what is the expected number of purchases?

Accepted Answer

40

Answer

60

Answer

100

Answer

25

Question 7

Two events, A and B, are independent if:

Accepted Answer

The occurrence of one event does not affect the probability of the other event.

Answer

The events are equally likely to occur.

Answer

The events are mutually exclusive.

Question 8

A company has two divisions, North and South. The North division generates 70% of the company's revenue, and the South division generates the remaining 30%. What is the probability that a randomly selected customer is from the North division?

Accepted Answer

0.7

Answer

0.9

Answer

0.5

Answer

0.3

Question 9

Which of the following is NOT an axiom of probability?

Accepted Answer

The probability of an event can be negative.

Answer

The probability of an event is between 0 and 1.

Answer

The probability of the sample space is 1.

Question 10

A company produces light bulbs with a 1% defective rate. If a box contains 100 bulbs, what is the expected number of defective bulbs?

Accepted Answer

1

Answer

10

Answer

Cannot be determined

Answer

0.01

Question 11

A marketing team is planning a campaign. They estimate a 20% chance of reaching their target audience with their message. If they spend $10,000 on the campaign and expect to generate $30,000 in revenue if successful, what is the expected value of the campaign?

Accepted Answer

$4,000

Answer

$20,000

Answer

$30,000

Answer

$10,000

Question 12

A manufacturing plant produces widgets. The probability that a widget is defective is 0.05. What is the probability that a randomly selected widget is NOT defective?

Accepted Answer

0.95

Answer

0.5

Answer

0.05

Question 13

A company is developing a new product. They estimate a 60% chance of the product being successful. If successful, they expect to make a profit of $1 million. If unsuccessful, they will lose $500,000. What is the expected profit from developing the product?

Accepted Answer

$300,000

Answer

$1,000,000

Answer

$500,000

Question 14

A survey of 500 customers revealed that 100 prefer a particular product. What is the probability that a randomly selected customer prefers this product?

Accepted Answer

0.2

Answer

0.5

Answer

0.1

Answer

1

Question 15

A company is conducting a survey to understand customer preferences for a new product. They randomly select 500 customers from their database. Which type of probability is being used in this scenario?

Accepted Answer

Empirical Probability

Answer

Prior Probability

Answer

Theoretical Probability

Answer

Conditional Probability

Question 16

A manufacturing company produces light bulbs. They know that 2% of their bulbs are defective. If a sample of 100 bulbs is selected, what is the expected number of defective bulbs in the sample?

Accepted Answer

2

Answer

20

Answer

10

Answer

5

Question 17

A company is offering a promotion where customers can win a prize by spinning a wheel with 10 equal sections. 3 sections are marked with 'Win a Gift Card', 5 sections with 'Try Again', and 2 sections with 'Free Product'. What is the probability of a customer winning a gift card?

Accepted Answer

3/10

Answer

1/5

Answer

1/2

Answer

3/5

Question 18

A sales manager observes that 80% of customers who purchase a product also purchase an extended warranty. If a customer purchases the product, what is the probability that they will also purchase the extended warranty?

Accepted Answer

80%

Answer

100%

Answer

20%

Answer

50%

Question 19

A customer service representative receives an average of 5 calls per hour. What is the probability that they will receive exactly 3 calls in the next hour?

Accepted Answer

This scenario can be modeled using a Poisson distribution.

Answer

3/5

Answer

5/12

Answer

1/5

Question 20

A company is conducting a quality control inspection on a batch of products. They randomly select 10 products from the batch. If the batch has a 5% defect rate, what is the probability that none of the selected products are defective?

Accepted Answer

This scenario can be modeled using a binomial distribution.

Answer

100%

Answer

50%

Answer

95%

Question 21

A bag contains 3 red balls, 2 blue balls, and 1 yellow ball. If a ball is drawn randomly from the bag, what is the probability of drawing a red ball?

Accepted Answer

3/6

Answer

1/3

Answer

1/2

Answer

2/3

Question 22

An experiment consists of rolling a six-sided die twice. What is the probability of rolling a sum of 7?

Accepted Answer

1/6

Answer

1/12

Answer

1/3

Answer

1/2

Question 23

A company estimates that there is a 20% chance of a new product succeeding. If the company launches 5 new products, what is the probability that at least one of them will succeed?

Accepted Answer

0.897

Answer

0.20

Answer

0.50

Question 24

A manufacturing process produces items with a 5% defect rate. What is the probability of selecting 4 consecutive items without any defects?

Accepted Answer

0.904

Answer

0.25

Answer

0.45

Answer

0.05

Question 25

Which of the following probability distributions has a mean of 0 and a standard deviation of 1?

Accepted Answer

Standard Normal Distribution

Answer

Poisson Distribution

Answer

Binomial Distribution

Answer

Uniform Distribution

Question 26

A survey of 100 customers revealed that 60% prefer product A. What is the 95% confidence interval for the true proportion of customers who prefer product A?

Accepted Answer

(0.53, 0.67)

Answer

(0.55, 0.70)

Answer

(0.45, 0.75)

Answer

(0.60, 0.80)

Question 27

A random sample of 50 students is selected from a population. The sample mean is 75 and the sample standard deviation is 10. What is the probability that the true population mean is less than 70?

Accepted Answer

0.0228

Answer

0.15

Answer

0.10

Answer

0.05

Question 28

Which of the following is NOT an assumption of the Central Limit Theorem?

Accepted Answer

The population must be normally distributed.

Answer

The sample size must be large enough.

Answer

The population must be finite.

Answer

The sample must be random.

Question 29

A company claims that their new software reduces customer wait times by an average of 10 minutes. A sample of 100 customers using the software shows an average wait time of 9 minutes with a standard deviation of 2 minutes. What is the p-value for testing the company's claim?

Accepted Answer

0.025

Answer

0.10

Answer

0.15

Answer

0.05

Question 30

A survey of 200 people found that 120 prefer coffee and 80 prefer tea. What is the probability that a randomly selected person from this group prefers coffee or tea?

Accepted Answer

1.0

Answer

0.60

Answer

0.80

Answer

0.90