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

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

Question 1

Which of the following best describes the Law of Large Numbers as illustrated by the coin toss graph in the first image?

Accepted Answer

As the number of tosses increases, the proportion of heads approaches 0.5.

Question 2

Suppose you roll two fair dice. What is the probability that the sum of the up-faces is 7? (Refer to the second image for all possible outcomes.)

Accepted Answer

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

Question 3

If event $$A is$$ 'rolling an even number' on a fair die, what is the probability of the complement of $$A ($$denoted $$A^c$$)?

Accepted Answer

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

Question 4

Which of the following statements about probability is TRUE?

Accepted Answer

The sum of probabilities of all outcomes in a sample space is always 1.

Question 5

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

Accepted Answer

$$0.8$$

Question 6

A student guesses on a three-question multiple-choice quiz, with a 20% chance of getting each question correct. What is the probability the student gets all three questions correct? (Refer to the tree diagram in the last image.)

Accepted Answer

$$0.008$$

Question 7

Which of the following is an example of subjective probability?

Accepted Answer

Estimating the chance of rain tomorrow based on your personal experience.

Question 8

If $$P(A) = 0.4$$ and $$P(B) = 0.3$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 9

Suppose the probability that a horse wins a race is $$0.4. $$What are the odds in favor of the horse winning?

Accepted Answer

$$\frac{2}{3} (or 2 to 3)$$

Question 10

If you toss three fair coins, what is the probability of getting exactly two heads?

Accepted Answer

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

Question 11

Which of the following is NOT a requirement for a probability model?

Accepted Answer

Each event must be equally likely.

Question 12

If $$P(A) = 0.7$$, what is $$P(A^c)$$?

Accepted Answer

$$0.3$$

Question 13

A university has the following student classification probabilities: First-Year: 0.25, Sophomore: 0.22, Junior: 0.23, Senior: 0.20, Graduate: 0.10. What is the probability that a randomly selected student is not a graduate student?

Accepted Answer

$$0.90$$

Question 14

Which of the following pairs of events are mutually exclusive (disjoint)?

Accepted Answer

Rolling a 3 and rolling a 5 on a single die.

Question 15

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

Accepted Answer

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

Question 16

Suppose 65% of students read the Lexington Herald-Leader, 51% read the Courier Journal, and 27% read both. What is the probability that a randomly selected student reads at least one of the two papers?

Accepted Answer

$$0.65 + 0.51 - 0.27 = 0.89$$

Question 17

Which of the following best describes the difference between odds and probability?

Accepted Answer

Probability is the chance of an event occurring, while odds compare the chance of an event occurring to it not occurring.

Question 18

If you roll a fair die, what is the probability of rolling a number greater than 4?

Accepted Answer

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

Question 19

Which of the following is an example of an empirical probability?

Accepted Answer

Calculating the probability of getting heads by flipping a coin 100 times and recording the results.

Chapter 5: Probability in Our Daily Lives – Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard