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

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

Question 1

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

Accepted Answer

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

Question 2

Which of the following statements about the probability of an event $$A is $$TRUE?

Accepted Answer

$$0 \leq P(A) \leq 1$$

Question 3

A die is rolled once. Let $$A be $$the event 'rolling an even number' and $$B be $$the event 'rolling a number greater than 4'. What is $$P(A \cap B)$$?

Accepted Answer

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

Question 4

If events $$A$$ and $$B$$ are disjoint, which formula correctly gives $$P(A \cup B)$$?

Accepted Answer

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

Question 5

A student is randomly chosen from a college where 65% own a car, 82% own a computer, and 55% own both. What is the probability that the student owns neither a car nor a computer?

Accepted Answer

$$0.08$$

Question 6

Which of the following is the correct formula for the probability of the complement of event $$A$$?

Accepted Answer

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

Question 7

You draw two cards from a deck with replacement. Let $$A be$$ 'first card is a spade' and $$B be$$ 'second card is a five'. Are $$A$$ and $$B$$ independent?

Accepted Answer

Yes, because the outcome of the first draw does not affect the second.

Question 8

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

Accepted Answer

$$0.2$$

Question 9

A family has two children. Let $$A be$$ 'first child is a boy' and $$B be$$ 'second child is a boy'. Are $$A$$ and $$B$$ disjoint?

Accepted Answer

No, because both children can be boys.

Question 10

Suppose you roll a fair die. What is the probability of rolling a number less than 5?

Accepted Answer

$$\frac{4}{6}$$

Question 11

Which of the following is NOT a property of probability?

Accepted Answer

Probability of any event can be negative.

Question 12

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

Accepted Answer

$$0.7$$

Question 13

In a statistics class, there are 35 domestic and 45 international students. If you choose a student at random and know the student is international, what is the probability she does NOT live in Vancouver if 24 international students live in Vancouver?

Accepted Answer

$$\frac{21}{45}$$

Question 14

Which of the following is the correct formula for conditional probability $$P(B|A)$$?

Accepted Answer

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

Question 15

You toss a fair coin twice. What is the probability of getting at least one head?

Accepted Answer

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

Question 16

If events $$A$$ and $$B$$ are independent, which of the following must be true?

Accepted Answer

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

Question 17

A die is rolled. Let $$A be$$ 'rolling a 2 or 4' and $$B be$$ 'rolling an even number'. Are $$A$$ and $$B$$ disjoint?

Accepted Answer

No, because both events can occur together.

Question 18

Suppose you choose 3 students at random with replacement from a class where 45 out of 80 are international students. What is the probability that at least one of the chosen students is international?

Accepted Answer

$$1 - \left(\frac{35}{80}\$$right)^3$$

Question 19

Which of the following is NOT a way to check if two events $$A$$ and $$B$$ are independent?

Accepted Answer

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

Fundamental Probability Concepts and Rules

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