Q: Which of the following is true for independent events $$A$$ and $$B$$?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Q: A box contains 6 defective and 94 non-defective TVs. If 5 TVs are selected at random, what is the number of ways exactly 2 defective TVs can be chosen?

$$\binom{6}{2} \times \binom{94}{3}$$

Question 1

A fair six-sided die is rolled twice. What is the probability that both rolls result in a 3?

Accepted Answer

$$\frac{1}{36}$$

Question 2

Which of the following statements best describes mutually exclusive events?

Accepted Answer

They have no outcomes in common.

Question 3

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 4

A bag contains 5 red balls and 7 blue balls. If one ball is drawn at random, what is the probability it is blue?

Accepted Answer

$$\frac{7}{12}$$

Question 5

Which formula gives the probability of the complement of event $$E$$?

Accepted Answer

$$P(E^c) = 1 - P(E)$$

Question 6

Suppose $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A 	ext{ and } B) = 0.1. $$What is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.6$$

Question 7

A university survey finds that 60% of students own a laptop, 30% own a tablet, and 20% own both. What is the probability that a randomly selected student owns either a laptop or a tablet?

Accepted Answer

$$0.9$$

Question 8

If $$P(B|A) = 0.5$$ and $$P(A) = 0.2$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.1$$

Question 9

Which of the following is true for independent events $$A$$ and $$B$$?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 10

A contingency table shows that 40% of faculty are under 40 years old, and 10% of all faculty are both under 40 and full professors. What is the conditional probability that a faculty member is a full professor given they are under 40?

Accepted Answer

$$0.25$$

Question 11

A medical test for a disease is 99% accurate. If 1% of the population has the disease, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$0.0199$$

Question 12

How many ways can a committee of 3 be chosen from a group of 10 people?

Accepted Answer

$$\frac{10!}{3!7!}$$

Question 13

If a password consists of 4 letters (A-Z) and repetition is allowed, how many possible passwords are there?

Accepted Answer

$$26^4$$

Question 14

Which of the following is the formula for the number of permutations of $$r$$ objects from a collection of $$m$$ objects?

Accepted Answer

$$\frac{m!}{(m-r)!}$$

Question 15

A box contains 6 defective and 94 non-defective TVs. If 5 TVs are selected at random, what is the number of ways exactly 2 defective TVs can be chosen?

Accepted Answer

$$\binom{6}{2} 	imes \binom{94}{3}$$

Question 16

Which rule allows you to find $$P(B)$$ when $$B$$ can occur with several mutually exclusive and exhaustive events $$A_1$$, $$A_2$$, ..., A_n$$?

Accepted Answer

The Rule of Total Probability

Question 17

If $$P(A|B) = 0.3$$, $$P(B) = 0.2$$, and $$P(A) = 0.1$$, what is $$P(B|A)$$ using Bayes’s Rule?

Accepted Answer

$$0.6$$

Question 18

Which of the following best describes the sample space of an experiment?

Accepted Answer

The set of all possible outcomes

Question 19

If two events $$A$$ and $$B$$ are independent, which of the following is always true?

Accepted Answer

$$P(A|B) = P(A)$$

Question 20

A deck of cards has 52 cards. What is the probability of drawing an ace or a king in a single draw?

Accepted Answer

$$\frac{8}{52}$$

Probability Concepts – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard