Q: Which of the following statements is TRUE about independent events?

If A and B are independent, then $$P(A \cap B) = P(A) \times P(B)$$

Question 1

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

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

Question 2

If you draw a single card from a standard deck of 52 cards, what is the probability that it is a heart?

Accepted Answer

$$\frac{1}{4}$$

Question 3

Suppose you toss a fair coin three times. What is the probability of getting exactly two heads?

Accepted Answer

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

Question 4

A box contains 4 red balls and 3 white balls. If two balls are drawn one after another without replacement, what is the probability that both are white?

Accepted Answer

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

Question 5

Which of the following is the correct formula for the probability of the union of two events A and B?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 6

If the probability of event A is 0.45, what is the probability that event A does NOT occur?

Accepted Answer

$$0.55$$

Question 7

Two dice are rolled. What is the probability that the sum is 7 or 11?

Accepted Answer

$$\frac{2}{9}$$

Question 8

Which of the following statements is TRUE about independent events?

Accepted Answer

If A and B are independent, then $$P(A \cap B) = P(A) 	imes P(B)$$

Question 9

A Venn diagram shows that 35% of students have a cat, 30% have a dog, and 10% have both. What is the probability that a randomly selected student has either a cat or a dog?

Accepted Answer

$$0.70$$

Question 10

If events A and B are mutually exclusive, which of the following is TRUE?

Accepted Answer

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

Question 11

A card is drawn from a standard deck. What is the probability that it is either a king or a heart?

Accepted Answer

$$\frac{4}{52} + \frac{13}{52} - \frac{1}{52}$$

Question 12

If the probability of event A is 0.6 and the probability of event B is 0.5, and A and B are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.3$$

Question 13

Suppose you roll two dice. What is the probability that the sum is 5, given that the first die shows a 2?

Accepted Answer

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

Question 14

Which of the following best describes a sample space?

Accepted Answer

A list of all possible outcomes of a random phenomenon

Question 15

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

Accepted Answer

$$0.7$$

Question 16

A probability model assigns probabilities to:

Accepted Answer

Events of a random phenomenon

Question 17

If the probability of drawing a heart from a deck of cards is $$\frac{1}{4}$$, what is the probability of NOT drawing a heart?

Accepted Answer

$$\frac{3}{4}$$

Question 18

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

Accepted Answer

Drawing two cards from a deck without replacement

Question 19

If $$P(A|B) = \frac{2}{3}$$ and $$P(B) = \frac{1}{2}$$, what is $$P(A \cap B)$$?

Accepted Answer

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

Question 20

A tree diagram is most useful for:

Accepted Answer

Representing all possible outcomes and their probabilities in multi-step experiments

Fundamentals of Probability in Statistics

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