Q: If two scales are randomly selected with replacement from 810, and 102 are defective, what is the probability both are defective?

$$\frac{102}{810} \times \frac{102}{810}$$

Question 1

Suppose you roll a fair six-sided die. Let event $$A be $$rolling an even number. What is the probability of event $$A$$ occurring?

Accepted Answer

$$\frac{1}{2}$$

Question 2

A wheel is spun with 8 equal slices labeled 1P, 2Y, 3Y, 4B, 5B, 6B, 7R, 8P. What is the sample space $$S$$ for this experiment?

Accepted Answer

$$S = \{1P, 2Y, 3Y, 4B, 5B, 6B, 7R, 8P\}$$

Question 3

Given the Venn diagram where $$A \subseteq B \subseteq S$$, which of the following statements is true?

Accepted Answer

Every outcome in $$A is $$also in $$B.$$

Question 4

If two events $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cap B)$$?

Accepted Answer

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

Question 5

A survey of 1,010 adults found that 202 smoke. What is the probability that a randomly selected adult does NOT smoke?

Accepted Answer

$$1 - \frac{202}{1010}$$

Question 6

In a sample of 20 people, 13 are female and 7 are male. If 8 own a pet, what is the probability that a randomly selected person owns a pet?

Accepted Answer

$$\frac{8}{20}$$

Question 7

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

Accepted Answer

$$0.9$$

Question 8

A contingency table shows 44 drug users with positive test results, 6 drug users with negative results, 90 non-users with positive results, and 860 non-users with negative results. What is the probability of randomly selecting a drug user?

Accepted Answer

$$\frac{44 + 6}{44 + 6 + 90 + 860}$$

Question 9

If two scales are randomly selected with replacement from 810, and 102 are defective, what is the probability both are defective?

Accepted Answer

$$\frac{102}{810} 	imes \frac{102}{810}$$

Question 10

Given the sample space $$S = \{1, 2, 3, 4, 5, 6\}$$, $$A = \{2, 4, 6\}$$, and $$B = \{2\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{2\}$$

Question 11

Suppose you spin the wheel shown (with 8 equal slices: 1P, 2Y, 3Y, 4B, 5B, 6B, 7R, 8P). What is the probability of getting a blue slice?

Accepted Answer

$$\frac{3}{8}$$

Question 12

If $$P(A) = 0.3$$ and $$P(B) = 0.4$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 13

A deck of cards: Let $$A be $$the event 'card is red', $$B be$$ 'card is a club'. Which is true?

Accepted Answer

$$A$$ and $$B$$ are mutually exclusive.

Question 14

Given the Titanic data: 197 first class survived, 122 first class died, 94 second class survived, 167 second class died, 151 third class survived, 476 third class died. What is the probability that a randomly selected passenger survived?

Accepted Answer

$$\frac{197 + 94 + 151}{197 + 122 + 94 + 167 + 151 + 476}$$

Question 15

If $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$, what does $$P(A|B)$$ represent?

Accepted Answer

The probability of $$A$$ occurring given $$B$$ has occurred.

Question 16

In a group of 20 people, 7 are male and 4 of those males do not own a pet. What is the probability that a randomly selected male does not own a pet?

Accepted Answer

$$\frac{4}{7}$$

Chapter 4: Probability – Structured Study Notes for Statistics Students

Study Guide - Practice Questions

Study Guide - Flashcards