Q: What is the formula for the probability of event A given event B has occurred?

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

Q: If events A and B are independent, what is the formula for the probability of both A and B occurring?

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

Q: Which formula would you use to find the probability of at least one blue ball being drawn from a box using a tree diagram?

$$ P(\text{at least one blue}) = 1 - P(\text{no blue}) $$

Question 1

Which of the following best describes a random phenomenon as discussed in Chapter 5?

Accepted Answer

An event where individual outcomes appear haphazard, but there is a regular distribution of outcomes when repeated many times.

Question 2

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

Accepted Answer

$$ \frac{13}{52} $$

Question 3

If you toss two coins, what is the sample space for the experiment?

Accepted Answer

$$ S = \{HH, HT, TH, TT\} $$

Question 4

Which property of probability states that the probability of all possible outcomes is one?

Accepted Answer

$$ P(S) = 1 $$

Question 5

What is the probability of rolling a 5 on a fair six-sided die?

Accepted Answer

$$ \frac{1}{6} $$

Question 6

If 45% of students have a cat, what is the probability that a randomly selected student does NOT have a cat?

Accepted Answer

$$ 0.55 $$

Question 7

If 20% of M&Ms are green and 35% are yellow, what is the probability that a randomly selected M&M is green OR yellow?

Accepted Answer

$$ 0.55 $$

Question 8

Given that 10% of students have both a cat and a dog, 45% have a cat, and 35% have a dog, what is the probability that a student has a cat OR a dog?

Accepted Answer

$$ 0.70 $$

Question 9

Which of the following pairs of events are independent?

Accepted Answer

Tossing heads on the first toss of a coin and tossing heads on the second toss.

Question 10

What is the formula for the probability of event A given event B has occurred?

Accepted Answer

$$ P(A|B) = \frac{P(A 	ext{ and } B)}{P(B)} $$

Question 11

In the context of the tree diagram for drawing balls from a box, what is the probability of drawing two white balls in succession from a box containing 3 red, 2 black, and 4 white balls?

Accepted Answer

$$ \frac{4}{9} \cdot \frac{3}{8} = \frac{1}{6} $$

Question 12

If events A and B are independent, what is the formula for the probability of both A and B occurring?

Accepted Answer

$$ P(A 	ext{ and } B) = P(A) \cdot P(B) $$

Question 13

Suppose you roll two dice. What is the probability that the sum is 7 or 11?

Accepted Answer

$$ \frac{8}{36} $$

Question 14

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be greater than one.

Question 15

If you draw two balls from the box (3 red, 2 black, 4 white), what is the probability that the first ball is black and the second ball is red?

Accepted Answer

$$ \frac{2}{9} \cdot \frac{3}{8} = \frac{6}{72} = \frac{1}{12} $$

Question 16

Which formula would you use to find the probability of at least one blue ball being drawn from a box using a tree diagram?

Accepted Answer

$$ P(	ext{at least one blue}) = 1 - P(	ext{no blue}) $$

Question 17

If the probability of event A is 0.3 and the probability of event B is 0.4, and they are disjoint, what is the probability of A or B?

Accepted Answer

$$ 0.7 $$

Question 18

If the probability of event A is 0.5 and the probability of event B is 0.6, and the probability of both A and B is 0.2, what is the probability of A or B?

Accepted Answer

$$ 0.5 + 0.6 - 0.2 = 0.9 $$

Question 19

Which of the following is an example of a dependent event?

Accepted Answer

Drawing an ace from a deck, then drawing another ace from the same deck.

Chapter 5: Probability – Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards