Q: If you roll a fair six-sided die twice, what is the probability that both rolls result in a 6?

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

Q: If the probability of answering the first question correctly is 0.63 and the second correctly is 0.69, but the probability of both is 0.58, are the events independent?

No, because $$0.63 \times 0.69 \neq 0.58$$

Q: Which rule is used to find the probability that either event A or event B occurs?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Question 1

Which of the following best describes the law of large numbers in the context of random phenomena?

Accepted Answer

It states that as the number of trials increases, the proportion of times an event occurs gets closer to a specific value.

Question 2

A coin is tossed 100 times and lands on heads 53 times. What is the relative frequency of heads?

Accepted Answer

$$\frac{53}{100} = 0.53$$

Question 3

Which of the following statements about independent trials is correct?

Accepted Answer

The outcome of any one trial is not affected by the outcome of any other trial.

Question 4

If you roll a fair six-sided die twice, what is the probability that both rolls result in a 6?

Accepted Answer

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

Question 5

A swim team must select 2 assistants from a group of 4. What is the probability that a particular pair is chosen?

Accepted Answer

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

Question 6

Which formula gives the number of ways to choose r objects from n distinct objects without regard to order?

Accepted Answer

$$nCr = \frac{n!}{r!(n-r)!}$$

Question 7

Suppose you flip a coin three times. What is the size of the sample space?

Accepted Answer

$$2^3 = 8$

Question 8

If the probability of event A is 0.4, what is the probability of its complement?

Accepted Answer

$$1 - 0.4 = 0.6$$

Question 9

Given $$P(A) = 0.5$$, $$P(B) = 0.6$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.5 + 0.6 - 0.2 = 0.9$$

Question 10

A student guesses on a three-question multiple-choice quiz, each with 5 options. What is the probability the student gets all three correct?

Accepted Answer

$$\left(\frac{1}{5}\$$right)^3$$ = 0.008$$

Question 11

Which of the following is an example of a subjective probability?

Accepted Answer

A doctor estimates the chance of recovery based on experience and available information.

Question 12

If events A and B are disjoint, which of the following is true?

Accepted Answer

$$P(A 	ext{ and } B) = 0$$

Question 13

A contingency table shows that 1,405 out of 145,781 tax returns were audited. What is the probability that a randomly selected return was audited?

Accepted Answer

$$\frac{1405}{145781} \approx 0.0096$$

Question 14

Which of the following best describes the sample space for flipping two coins?

Accepted Answer

S = {(H, H), (H, T), (T, H), (T, T)}

Question 15

If the probability of answering the first question correctly is 0.63 and the second correctly is 0.69, but the probability of both is 0.58, are the events independent?

Accepted Answer

No, because $$0.63 	imes 0.69 
eq 0.58$$

Question 16

A family has two children. What is the probability that at least one child is a girl, assuming all gender combinations are equally likely?

Accepted Answer

$$0.75$$

Question 17

Which rule is used to find the probability that either event A or event B occurs?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 18

If you select 3 students from a class of 10, how many possible combinations are there?

Accepted Answer

$$\frac{10!}{3!7!} = 120$$

Question 19

Which of the following is NOT a property of probability?

Accepted Answer

The probability of any event is always greater than 1.

(Lecture 10) Probability in Our Daily Lives: Fundamental Concepts and Applications

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