Q: If the probability of a student guessing a question correctly is $$0.2$$, what is the probability that the student answers all three questions correctly by guessing?

$$P(CCC) = 0.2 \times 0.2 \times 0.2 = 0.008$$

Q: If two events A and B are independent, which formula gives the probability that both A and B occur?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Q: If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \text{ and } B) = 0.2$$, what is $$P(A \text{ or } B)$$?

$$P(A \text{ or } B) = 0.4 + 0.5 - 0.2 = 0.7$$

Q: A student answers two multiple choice questions. The probability of getting both correct is 0.58, the probability of getting the first correct is 0.63, and the probability of getting the second correct is 0.69. Are the events 'first correct' and 'second correct' independent?

No, because $$0.63 \times 0.69 = 0.43 \neq 0.58$$

Question 1

Which of the following best describes the Law of Large Numbers as it relates to flipping a fair coin?

Accepted Answer

As the number of coin tosses increases, the proportion of heads will get closer to 0.5.

Question 2

A basketball player shoots three free throws. What is the sample space for the number of baskets made?

Accepted Answer

$$S = \{0, 1, 2, 3\}$$

Question 3

If the probability of a student guessing a question correctly is $$0.2$$, what is the probability that the student answers all three questions correctly by guessing?

Accepted Answer

$$P(CCC) = 0.2 	imes 0.2 	imes 0.2 = 0.008$$

Question 4

Which of the following is NOT a random phenomenon?

Accepted Answer

A student gets an answer correct after hours of studying.

Question 5

Given the table of taxpayers, what is the probability that a randomly selected taxpayer has an income of $100,000 or more?

Accepted Answer

$$P = \frac{10700}{80200} = 0.133$$

Question 6

If two events A and B are independent, which formula gives the probability that both A and B occur?

Accepted Answer

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

Question 7

Which of the following statements about the complement of an event A is correct?

Accepted Answer

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

Question 8

Suppose you roll two fair dice. What is the probability that the sum is 5?

Accepted Answer

$$P = \frac{4}{36} = \frac{1}{9}$$

Question 9

If the probability that a child delivered in a certain hospital is a girl is 0.50, what does this mean?

Accepted Answer

Over a long period of time, there will be equal proportions of boys and girls born at that hospital.

Question 10

Which of the following best describes a subjective probability?

Accepted Answer

It is based on personal judgment or degree of belief, not on long-run frequency.

Question 11

A roulette wheel has 38 slots (18 red, 18 black, 2 green). What is the probability of landing on red?

Accepted Answer

$$P = \frac{18}{38}$$

Question 12

If events A and B are disjoint, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

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

Question 13

A nutrition researcher feeds a new diet to a rat and measures weight gain. What is the sample space for weight gain (in grams)?

Accepted Answer

$$S = [0, \infty]$$

Question 14

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.4 + 0.5 - 0.2 = 0.7$$

Question 15

A student answers two multiple choice questions. The probability of getting both correct is 0.58, the probability of getting the first correct is 0.63, and the probability of getting the second correct is 0.69. Are the events 'first correct' and 'second correct' independent?

Accepted Answer

No, because $$0.63 	imes 0.69 = 0.43 
eq 0.58$$

Question 16

Which of the following is an example of a discrete sample space?

Accepted Answer

The possible outcomes when rolling a single die.

Question 17

If you flip a coin 20 times and get heads every time, what is the probability of getting tails on the 21st flip?

Accepted Answer

$$P(	ext{tails}) = 0.5$$

Chapter 5: Probability in Our Daily Lives – Structured Study Notes

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