Probability in Business: Master Chance and Likelihood

Question 1

Which scale is used to measure the likelihood of an event occurring, ranging from 0 to 1?

Accepted Answer

Ratio scale

Answer

Interval scale

Answer

Ordinal scale

Answer

Nominal scale

Question 2

If you roll a standard six-sided die once, what is the experimental probability of rolling an even number?

Accepted Answer

1/2

Answer

1/6

Answer

1/3

Answer

2/3

Question 3

What is the probability of drawing a king from a standard deck of 52 cards?

Accepted Answer

1/13

Answer

1/52

Answer

1/4

Answer

1/2

Question 4

Two events are considered independent if the occurrence of one event:

Accepted Answer

Does not affect the probability of the other event.

Answer

Affects the probability of the other event.

Answer

Makes the other event more likely to occur.

Answer

Makes the other event less likely to occur.

Question 5

What is the probability of flipping a fair coin three times and getting tails all three times?

Accepted Answer

1/16

Answer

1/4

Answer

1/2

Answer

1/8

Question 6

Which of the following is NOT a factor to consider when calculating the conditional probability of an event?

Accepted Answer

The temperature

Answer

The event itself

Answer

The occurrence of another event

Answer

The probability of the event without the condition

Question 7

The probability of rolling a 6 on a standard six-sided die is calculated as:

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 8

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.3, what is the probability of both events occurring (P(A and B))?

Accepted Answer

0.12

Answer

0.7

Answer

0.2

Answer

0.4

Question 9

Which of the following is a characteristic of independent events?

Accepted Answer

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

Answer

The probability of both events occurring is always greater than 0.5.

Answer

The events cannot occur simultaneously.

Answer

The probability of one event is directly proportional to the probability of the other event.

Question 10

A probability distribution is a table or graph that shows the:

Accepted Answer

Possible outcomes of an experiment and their corresponding probabilities.

Answer

Average value of a set of data.

Answer

Standard deviation of a set of data.

Answer

Mean, median, and mode of a set of data.

Question 11

A company is considering launching a new product. The probability of success is estimated to be 0.6. What is the probability of failure?

Accepted Answer

0.4

Answer

0.2

Answer

0.8

Answer

0.6

Question 12

Which of the following statements about probability is correct?

Accepted Answer

Probability is a measure of the likelihood of an event occurring.

Answer

Probability can be used to predict the future with certainty.

Answer

Probability can be negative.

Answer

Probability is always equal to 1.

Question 13

Define theoretical probability.

Accepted Answer

The likelihood of an event based on equally likely outcomes

Answer

The probability of an event if it has occurred in the past

Answer

The probability of an event based on personal opinion

Answer

The probability of an event based on random chance

Question 14

A bag contains 5 red balls and 7 blue balls. If you draw one ball at random, what is the probability of drawing a red ball?

Accepted Answer

5/12

Answer

1/12

Answer

7/12

Answer

1/2

Question 15

If events A and B are independent, which of the following represents the probability of both A and B occurring (P(A ∩ B))?

Accepted Answer

P(A) * P(B)

Answer

P(A) + P(B)

Answer

P(A) - P(B)

Answer

P(A) / P(B)

Question 16

A bag contains 6 red balls, 4 blue balls, and 3 green balls. If two balls are drawn at random without replacement, what is the probability that the first ball is red and the second ball is blue?

Accepted Answer

2/15

Answer

1/10

Answer

1/15

Answer

1/3

Question 17

What is the main application of the binomial distribution?

Accepted Answer

Modeling the number of successes in independent experiments

Answer

Modeling the time until a certain event occurs

Answer

Modeling the height of individuals in a population

Answer

Modeling the weight of apples in a bag

Question 18

Which scale is used to measure probability?

Accepted Answer

0 to 1

Answer

-1 to 1

Answer

1 to 10

Answer

0 to 100%

Question 19

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.6, what is the probability of both A and B occurring?

Accepted Answer

0.2

Answer

0.1

Answer

0.4

Answer

0.8

Question 20

What is the probability of rolling a 6 on a standard six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 21

Two events, A and B, are independent. The probability of event A occurring is 0.4 and the probability of event B occurring is 0.6. What is the probability of both events occurring?

Accepted Answer

0.24

Answer

0.1

Answer

0.64

Answer

1.0

Question 22

A survey of 100 customers found that 60% of them preferred Product A over Product B. What is the probability that a randomly selected customer prefers Product A?

Accepted Answer

0.6

Answer

0.3

Answer

0.4

Answer

0.7

Question 23

What is the probability of getting at least one head when flipping a coin twice?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

0

Question 24

Which of the following is NOT a scale of probability?

Accepted Answer

-1 to 1

Answer

0 to 1

Answer

0% to 100%

Answer

1% to 99%

Question 25

Two events, A and B, are mutually exclusive. What is the probability of either event occurring?

Accepted Answer

P(A) + P(B)

Answer

P(A) - P(B)

Answer

P(A) * P(B)

Answer

P(A) / P(B)

Question 26

A company has a 60% chance of meeting its sales target in the next quarter. What is the probability that the company will not meet its sales target?

Accepted Answer

0.4

Answer

0.5

Answer

0.6

Answer

1.0

Question 27

You toss a coin three times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

1/2

Answer

1/4

Answer

3/4

Question 28

If the probability of event A is 0.4 and the probability of event B is 0.6, what is the probability of both events occurring?

Accepted Answer

0.24

Answer

0.8

Answer

0.2

Answer

1.0

Question 29

Two dice are rolled. What is the probability of getting a double (both dice showing the same number)?

Accepted Answer

1/36

Answer

1/6

Answer

1/12

Answer

1/2

Question 30

A fair six-sided die is rolled. What is the probability of getting a number greater than 3?

Accepted Answer

5/6

Answer

1/2

Answer

1/3

Answer

1/6

Question 31

A company is launching a new product. Based on market research, the probability of success is estimated to be 0.6. What is the probability of failure?

Accepted Answer

0.4

Answer

0.6

Answer

1.0

Answer

Cannot be determined

Question 32

Independent events are events where:

Accepted Answer

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

Answer

The probability of both events occurring is equal to their individual probabilities multiplied together.

Answer

The events are mutually exclusive.

Question 33

In a multiple-choice test with 5 questions and 4 possible answers per question, if a student randomly guesses each answer, what is the probability of answering all 5 questions correctly?

Accepted Answer

1/1024

Answer

1/25

Answer

1/5

Answer

1/125

Question 34

Which of the following is NOT a characteristic of a probability distribution?

Accepted Answer

The sum of probabilities is less than 1.

Answer

A normal distribution

Answer

A binomial distribution

Question 35

For a binomial distribution, the mean is given by:

Accepted Answer

np

Answer

np/2

Answer

n/p

Answer

np + 1

Question 36

Which of the following is an example of a subjective probability?

Accepted Answer

The probability of winning a lottery.

Answer

The probability of drawing a heart from a deck of cards.

Answer

The probability of rolling a 6 on a die.

Answer

The probability of getting heads when flipping a coin.

Question 37

Conditional probability refers to:

Accepted Answer

The probability of an event occurring given that another event has already occurred.

Answer

The probability of an event occurring independently of another event.

Answer

The probability of an event occurring before another event.

Question 38

The probability of an event not occurring is:

Accepted Answer

1 - Probability of the event

Answer

Probability of the event minus 1

Answer

Probability of the event multiplied by -1

Answer

Probability of the event divided by 2

Question 39

Events A and B are independent. If P(A) = 0.3 and P(B) = 0.4, what is P(A and B)?

Accepted Answer

0.12

Answer

0.08

Answer

0.24

Answer

0.16

Question 40

What is the probability of getting a 'head' when flipping a fair coin?

Accepted Answer

1/2

Answer

1/4

Answer

1/5

Answer

1/3

Question 41

What is the probability scale used in business?

Accepted Answer

0 to 1

Answer

-1 to 1

Answer

-10 to 10

Answer

0 to 10

Question 42

What is the expected value of a discrete probability distribution?

Accepted Answer

The mean of the distribution

Answer

The mode of the distribution

Answer

The standard deviation of the distribution

Answer

The median of the distribution

Question 43

A survey revealed that 60 people preferred brand A, 30 preferred brand B, and 10 preferred both brands. What is the probability that a person chosen at random preferred either brand A or brand B?

Accepted Answer

0.8

Answer

0.4

Answer

0.2

Answer

0.6

Question 44

Which of the following statements is true about independent events?

Accepted Answer

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

Answer

The occurrence of one event decreases the probability of the other event

Answer

The occurrence of one event increases the probability of the other event

Question 45

A company's sales data over the past year can be represented by the following probability distribution:
Sales (in thousands) | Probability
---------------------------
10 | 0.2
20 | 0.3
30 | 0.4
40 | 0.1
What is the expected value of sales?

Accepted Answer

26

Answer

22

Answer

30

Answer

34

Question 46

Which of the following scales is used to measure the probability of an event?

Accepted Answer

0 to 1

Answer

1 to 10

Answer

0 to 100

Answer

-1 to 1

Question 47

A marketing campaign is expected to reach 50% of the target audience. If the audience consists of 100,000 people, approximately how many people are expected to be reached by the campaign?

Accepted Answer

50,000

Answer

75,000

Answer

25,000

Answer

100,000

Question 48

A survey found that 75% of customers prefer brand A. What is the probability that, out of 12 randomly selected customers, more than 9 will prefer brand A?

Accepted Answer

0.232

Answer

0.25

Answer

0.75

Question 49

A bag contains 6 red balls and 4 blue balls. Two balls are drawn without replacement. What is the probability that at least one ball is red?

Accepted Answer

11/15

Answer

1/2

Answer

2/5

Answer

6/10

Question 50

Two events, A and B, are independent. If P(A) = 0.45 and P(B) = 0.35, what is P(A and B)?

Accepted Answer

0.1575

Answer

0.7

Answer

0.45

Answer

0.1