Question 1

Suppose you flip two fair coins. What is the probability that both coins show the same face (either both heads or both tails)?

Accepted Answer

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

Question 2

You roll two fair six-sided dice. What is the probability that the numbers on the two dice do NOT match?

Accepted Answer

$$\frac{5}{6}$$

Question 3

Which of the following best describes mutually exclusive (disjoint) events?

Accepted Answer

Events that cannot happen at the same time

Question 4

A deck of 52 cards contains 13 cards per suit. What is the probability of drawing a face card (King, Queen, or Jack) from a standard deck?

Accepted Answer

$$\frac{12}{52}$$

Question 5

If the probability that it will rain tomorrow is 0.4, what is the probability that it will NOT rain?

Accepted Answer

$$1 - 0.4 = 0.6$$

Question 6

Which formula represents the probability of the complement of event $$A$$?

Accepted Answer

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

Question 7

The Law of Large Numbers states that as the number of trials increases, the experimental probability will:

Accepted Answer

Approach the theoretical probability

Question 8

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.8$$

Question 9

Given the tree diagram where $$P(	ext{rain}) = 0.25$$, $$P(	ext{late} | 	ext{rain}) = 0.2$$, and $$P(	ext{not late} | 	ext{rain}) = 0.8$$, what is the probability that it rains and you are not late?

Accepted Answer

$$0.25 	imes 0.8 = 0.2$$

Question 10

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

Accepted Answer

$$\frac{6}{36} = \frac{1}{6}$$

Question 11

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 12

In a large residence hall, 30% of students speak Spanish, 20% speak Chinese, and 10% speak both. What is the probability that a randomly selected student speaks Spanish or Chinese?

Accepted Answer

$$0.3 + 0.2 - 0.1 = 0.4$$

Question 13

If $$P(	ext{Spanish} \mid 	ext{Chinese}) = 0.5$$, what does this probability represent?

Accepted Answer

The probability a student speaks Spanish given they speak Chinese

Question 14

A child is tested for handedness. The probability the child is actually left-handed is 0.10, and the probability a left-handed child tests as left-handed is 1. What is the probability that a randomly selected child is actually left-handed and tests as left-handed?

Accepted Answer

$$0.10 	imes 1 = 0.10$$

Question 15

Which of the following is an example of complementary events?

Accepted Answer

It rains or it does not rain

Question 16

If $$P(A|B) = 0.3$$, what does this mean?

Accepted Answer

The probability that event $$A$$ occurs given that event $$B$$ has occurred is 0.3

Question 17

A roulette wheel has 18 red, 18 black, and 2 green slots. What is the probability of landing on green?

Accepted Answer

$$\frac{2}{38}$$

Question 18

If you flip a coin 10 times and get 7 heads, what is the experimental probability of getting heads?

Accepted Answer

$$\frac{7}{10}$$

Question 19

Which of the following is NOT a valid sample space for a random experiment?

Accepted Answer

The set of all even numbers

Introduction to Probability: Key Concepts and Applications

Guida di studio - Domande di pratica

Study guide - Flashcard