Q: A bag contains 4 red balls and 6 blue balls. Two balls are drawn one after another without replacement. What is the probability that both balls are red?

$$ \frac{4}{10} \times \frac{3}{9} = 0.133 $$

Q: Suppose a model number consists of a letter (A, B, C, or D) followed by two digits (0–9). How many different model numbers are possible?

$$ 4 \times 10 \times 10 = 400 $$

Q: A bank uses Bayes’ Theorem to update the probability that a customer has a credit score less than 600 given that they are late on a payment. If the prior probability is 0.25, the conditional probability of being late given a score less than 600 is 0.40, and the total probability of being late is 0.16, what is the revised probability?

$$ \frac{0.25 \times 0.40}{0.16} = 0.625 $$

Question 1

Which of the following best describes the classical method of assigning probability?

Accepted Answer

It is used when all possible outcomes are known and equally likely.

Question 2

A company surveyed 400 employees and found that 120 commute by train. What is the empirical probability that a randomly selected employee commutes by train?

Accepted Answer

$$ \frac{120}{400} = 0.30 $$

Question 3

If the probability of an event A is 0.7, what is the probability of the complement of A?

Accepted Answer

$$ 0.3 $$

Question 4

A die is rolled once. What is the probability of rolling a number greater than 4?

Accepted Answer

$$ \frac{2}{6} = 0.333 $$

Question 5

Which of the following is an example of subjective probability?

Accepted Answer

Estimating the probability of rain tomorrow based on your experience.

Question 6

Given the contingency table below, what is the probability that a randomly selected student is a female freshman? (Refer to the table with 17 female freshmen out of 50 total students.)

Accepted Answer

$$ \frac{17}{50} = 0.34 $$

Question 7

If Events A and B are mutually exclusive, which of the following is true?

Accepted Answer

$$ P(A \cap B) = 0 $$

Question 8

A restaurant finds that 70 out of 200 customers who ordered meat were satisfied. What is the probability that a randomly selected customer both ordered meat and was satisfied?

Accepted Answer

$$ \frac{70}{200} = 0.35 $$

Question 9

If $$ P(A) = 0.4 $$, $$ P(B) = 0.5 $$, and $$ P(A \cap B) = 0.2 $$, what is $$ P(A \cup B) $$?

Accepted Answer

$$ 0.4 + 0.5 - 0.2 = 0.7 $$

Question 10

A student is selected at random. What is the probability that the student is either a junior or a female, given the table with 6 juniors and 28 females out of 50 students, with 2 female juniors?

Accepted Answer

$$ \frac{6 + 28 - 2}{50} = 0.64 $$

Question 11

If $$ P(A|B) = 0.632 $$ and $$ P(A) = 0.55 $$, what can you conclude about the relationship between A and B?

Accepted Answer

A and B are dependent events.

Question 12

A bag contains 4 red balls and 6 blue balls. Two balls are drawn one after another without replacement. What is the probability that both balls are red?

Accepted Answer

$$ \frac{4}{10} 	imes \frac{3}{9} = 0.133 $$

Question 13

Which of the following statements about mutually exclusive and independent events is correct?

Accepted Answer

Mutually exclusive events are always dependent.

Question 14

A company classifies its customers into three credit score categories: less than 600, 600–700, and above 700. If 25% of customers have scores less than 600, and 40% of them are late on payments, what is the joint probability that a randomly selected customer has a score less than 600 and is late on payment?

Accepted Answer

$$ 0.25 	imes 0.40 = 0.10 $$

Question 15

Suppose a model number consists of a letter (A, B, C, or D) followed by two digits (0–9). How many different model numbers are possible?

Accepted Answer

$$ 4 	imes 10 	imes 10 = 400 $$

Question 16

How many permutations are there if you select and arrange 2 letters from A, B, C, D?

Accepted Answer

$$ \frac{4!}{(4-2)!} = 12 $$

Question 17

How many combinations are there if you select 2 letters from A, B, C, D (order does not matter)?

Accepted Answer

$$ \frac{4!}{2!2!} = 6 $$

Question 18

A bank uses Bayes’ Theorem to update the probability that a customer has a credit score less than 600 given that they are late on a payment. If the prior probability is 0.25, the conditional probability of being late given a score less than 600 is 0.40, and the total probability of being late is 0.16, what is the revised probability?

Accepted Answer

$$ \frac{0.25 	imes 0.40}{0.16} = 0.625 $$

Chapter 4: Introduction to Probability – Business Statistics Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards