Q: A deck of 52 cards: What is the probability of drawing two spades in a row without replacement?

$$\frac{13}{52} \times \frac{12}{51} \approx 0.0588$$

Question 1

Which of the following best describes the sample space $$S in $$probability theory?

Accepted Answer

The set of all possible outcomes of a random experiment.

Question 2

A fair die is rolled twice. What is the probability that the sum of the two dice equals 7?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Suppose you flip a fair coin three times. What is the probability of getting at least one head?

Accepted Answer

$$1 - \left(\frac{1}{2}\$$right)^3$$ = 1 - \frac{1}{8} = \frac{7}{8}$$

Question 5

A diagnostic test for a disease has a positive result in 1355 out of 5282 cases. What is the empirical probability of a positive result?

Accepted Answer

$$\frac{1355}{5282} \approx 0.257$$

Question 6

Which rule should be used to find the probability that either event $$A or $$event $$B$$ occurs (not necessarily exclusively)?

Accepted Answer

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

Question 7

If the probability of drawing an ace from a standard deck is $$\frac{4}{52}$$, what is the probability of drawing an ace of spades?

Accepted Answer

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

Question 8

A student randomly guesses on a three-question multiple-choice quiz, each with five options. What is the probability the student gets all three correct?

Accepted Answer

$$(0.20)^3 = 0.008$

Question 9

Which of the following statements about probability is FALSE?

Accepted Answer

Probability can be greater than 1 for some events.

Question 10

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

Accepted Answer

$$0.3 	imes 0.5 = 0.15$$

Question 11

In a contingency table, how do you calculate the conditional probability $$P(A|B)$$?

Accepted Answer

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

Question 12

A deck of 52 cards: What is the probability of drawing two spades in a row without replacement?

Accepted Answer

$$\frac{13}{52} 	imes \frac{12}{51} \approx 0.0588$$

Question 13

Which of the following is a subjective probability?

Accepted Answer

A personal belief about the likelihood of rain tomorrow based on current information.

Question 14

If $$P(A|B) = P(A)$$, what does this imply about events $$A$$ and $$B$$?

Accepted Answer

Events $$A$$ and $$B$$ are independent.

Question 15

In the birthday problem, what is the probability that at least two students in a group of 28 share a birthday?

Accepted Answer

$$1 - 0.43 = 0.57$$

Question 16

Which of the following is the complement rule for probability?

Accepted Answer

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

Question 17

A tennis player faults on the first serve with probability $$0.38$$, and faults on the second serve given a first fault with probability $$0.045. $$What is the probability of a double fault?

Accepted Answer

$$0.38 	imes 0.045 = 0.017$$

Question 18

Which of the following is NOT a primary axiom of probability?

Accepted Answer

The probability of any event can be negative.

Question 19

If you have a contingency table, how do you find the probability that a randomly selected student is moderate and attends church occasionally?

Accepted Answer

$$P(	ext{Moderate} \cap 	ext{Occasionally}) = \frac{34}{100} = 0.34$$

Probability Concepts in Statistics: Foundations and Applications

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