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

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

Question 1

Which of the following best describes subjective probability?

Accepted Answer

A probability representing someone's personal degree of belief.

Question 2

Suppose you roll a fair six-sided die. What is the theoretical probability of rolling a number greater than 4?

Accepted Answer

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

Question 3

If $$ P(A) = 0.4 $$ and $$ P(B) = 0.5 $$, and A and B are mutually exclusive, what is $$ P(A \cup B) $$?

Accepted Answer

$$ 0.9 $$

Question 4

A medical test for a disease returns positive in 95% of cases when the disease is present and 2% of cases when the disease is absent. If 1% of the population has the disease, what type of probability is being described by the 95% figure?

Accepted Answer

Empirical probability

Question 5

Which of the following statements about independent events is correct?

Accepted Answer

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

Question 6

A weather forecaster estimates a 70% chance of rain tomorrow. This is an example of:

Accepted Answer

Subjective probability

Question 7

If $$ P(A) = 0.3 $$, $$ P(B) = 0.4 $$, and $$ P(A \cap B) = 0.12 $$, what is $$ P(A \cup B) $$?

Accepted Answer

$$ 0.58 $$

Question 8

Which of the following is NOT a requirement of a legitimate probability assignment?

Accepted Answer

Probabilities can be negative if the event is unlikely.

Question 9

A card is drawn from a standard deck. Let A be the event 'the card is a heart' and B be the event 'the card is a queen.' What is $$ P(A \cap B) $$?

Accepted Answer

$$ \frac{1}{52} $$

Question 10

If two events A and B are disjoint, which of the following must be true?

Accepted Answer

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

Question 11

A bag contains 5 red balls and 7 blue balls. If one ball is drawn at random, what is the probability it is red? (Use the probability assignment rule.)

Accepted Answer

$$ \frac{5}{12} $$

Question 12

If $$ P(A) = 0.6 $$ and $$ P(B) = 0.5 $$, and A and B are independent, what is $$ P(A \cap B) $$?

Accepted Answer

$$ 0.3 $$

Question 13

A company claims that the probability of their new battery lasting more than 2 years is 0.8, based on laboratory tests. This probability is best described as:

Accepted Answer

Empirical probability

Question 14

If $$ P(A) = 0.7 $$ and $$ P(B) = 0.2 $$, and A and B are disjoint, what is $$ P(A \cap B) $$?

Accepted Answer

$$ 0 $$

Question 15

Which rule would you use to find the probability that at least one of two independent events occurs?

Accepted Answer

Addition Rule

Question 16

A fair coin is tossed twice. What is the probability of getting at least one head?

Accepted Answer

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

Question 17

If $$ P(A) = 0.4 $$, what is the probability that event A does NOT occur?

Accepted Answer

$$ 0.6 $$

Question 18

Which of the following is an example of the complement rule?

Accepted Answer

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

Question 19

A student claims that the probability of getting a 7 when rolling a standard six-sided die is $$ \frac{1}{6} . $$What is wrong with this statement?

Accepted Answer

The probability is incorrect because 7 is not a possible outcome.

Question 20

If $$ P(A) = 0.5 $$ and $$ P(B) = 0.3 $$, and A and B are independent, what is $$ P(A \cap B^c) $$?

Accepted Answer

$$ 0.35 $$

Fundamental Concepts in Probability for Statistics

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