Q: Which formula correctly expresses the conditional probability of $$F$$ given $$E$$?

$$P(F|E) = \frac{P(E \text{ and } F)}{P(E)}$$

Question 1

Suppose you roll a fair six-sided die. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 2

A bag contains chips labeled 0 through 9. Let event $$E be$$ 'choose a number no greater than 2' and event $$F be$$ 'choose a number greater than or equal to 8'. Are $$E$$ and $$F$$ mutually exclusive?

Accepted Answer

Yes, because their intersection is the empty set.

Question 3

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$ for two independent events $$A$$ and $$B$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.15$$

Question 4

A counselor randomly samples 2000 student files and finds 984 are full-time students. What is the probability that a randomly selected student is full-time?

Accepted Answer

$$0.492$$

Question 5

Which of the following is NOT a rule of probability?

Accepted Answer

The probability of any event can be negative.

Question 6

If $$P(E) = 0.4$$ and $$P(F|E) = 0.5$$, what is $$P(E 	ext{ and } F)$$?

Accepted Answer

$$0.2$$

Question 7

A family has three children. What is the probability that exactly two are girls (in any order)?

Accepted Answer

$$0.375$$

Question 8

If $$P(E) = 0.7$$, what is $$P(E^c)$$, the probability of the complement of $$E$$?

Accepted Answer

$$0.3$$

Question 9

A box contains 12 transistors, 3 of which are defective. If 3 are selected at random, what is the probability that at least one is defective?

Accepted Answer

$$0.6182$$

Question 10

In a pizza restaurant, 95% of customers order pizza, and 65% order pizza and a salad. What is the probability that a customer orders a salad given they have already ordered pizza?

Accepted Answer

$$0.68$$

Question 11

How many different ways can 6 cross-country runners finish a race (all positions are distinct)?

Accepted Answer

$$720$$

Question 12

A bicycle shop owner has 12 mountain bikes and wants to select 5 for a show. How many different groups of 5 can be selected?

Accepted Answer

$$792$$

Question 13

If $$P(E) = 0.4$$, $$P(F) = 0.5$$, and $$P(E 	ext{ and } F) = 0.2$$, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$0.9$$

Question 14

Which formula correctly expresses the conditional probability of $$F$$ given $$E$$?

Accepted Answer

$$P(F|E) = \frac{P(E 	ext{ and } F)}{P(E)}$$

Question 15

A coin is flipped and a die is rolled. What is the probability of getting a tail and a 5?

Accepted Answer

$$\frac{1}{12}$$

Question 16

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the sample size increases, the relative frequencies of outcomes get closer to the theoretical probability.

Question 17

If two events $$E$$ and $$F$$ are independent, which of the following must be true?

Accepted Answer

$$P(E|F) = P(E)$$

Question 18

A box contains 12 transistors, 3 of which are defective. If 3 are selected at random, what is the probability that exactly two are defective?

Accepted Answer

$$0.1227$$

Question 19

Which of the following is the correct formula for the number of combinations of $$n$$ objects taken $$r at a $$time?

Accepted Answer

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

Question 20

If $$P(E) = 0.6$$ and $$P(F) = 0.5$$, and $$E$$ and $$F$$ are mutually exclusive, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$1.1 ($$but this is not possible, so the events cannot be mutually exclusive)

Probability Concepts and Rules: Study Notes for Statistics Students

Guida di studio - Domande di pratica

Study guide - Flashcard