Q: Suppose events A and B are not disjoint and $$P(A) = 0.4$$, $$P(B) = 0.5$$, $$P(A \text{ and } B) = 0.2. $$What is $$P(A \text{ or } B)$$?

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

Q: A fair die is rolled twice. What is the probability that both rolls result in a 6?

$$P(E) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$$

Question 1

A hospital records the number of patients admitted with flu symptoms each day. Over 200 days, 40 days had more than 10 admissions. Using the empirical method, what is the probability that on a randomly selected day, more than 10 patients are admitted?

Accepted Answer

$$P(E) = \frac{40}{200} = 0.2$$

Question 2

Which of the following best describes a chance experiment?

Accepted Answer

An experiment carried out under controlled conditions with unpredictable results.

Question 3

If you roll a fair six-sided die, what is the probability of getting a number greater than 4?

Accepted Answer

$$P(E) = \frac{2}{6} = \frac{1}{3}$$

Question 4

A student flips a fair coin twice. What is the probability of getting exactly one head?

Accepted Answer

$$P(E) = \frac{2}{4} = 0.5$$

Question 5

Which statement about the Law of Large Numbers is correct?

Accepted Answer

As the number of trials increases, the observed relative frequency approaches the theoretical probability.

Question 6

If $$P(A) = 0.7$$, what is the probability that event A does NOT occur?

Accepted Answer

$$P(A') = 1 - 0.7 = 0.3$$

Question 7

A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is either red or green?

Accepted Answer

$$P(E) = \frac{5+2}{10} = 0.7$$

Question 8

Which of the following is true about mutually exclusive (disjoint) events?

Accepted Answer

They cannot occur at the same time.

Question 9

Suppose events A and B are not disjoint and $$P(A) = 0.4$$, $$P(B) = 0.5$$, $$P(A 	ext{ and } B) = 0.2. $$What is $$P(A 	ext{ or } B)$$?

Accepted Answer

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

Question 10

A fair die is rolled twice. What is the probability that both rolls result in a 6?

Accepted Answer

$$P(E) = \frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$$

Question 11

Which of the following statements correctly distinguishes independent events from mutually exclusive events?

Accepted Answer

Independent events do not affect each other's probabilities, while mutually exclusive events cannot occur together.

Question 12

A deck of cards contains 52 cards. What is the probability of drawing either a heart or a king?

Accepted Answer

$$P(E) = \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13}$$

Question 13

If the probability of an unusual event is defined as less than 0.05, which of the following events is considered unusual?

Accepted Answer

An event with $$P(E) = 0.03$$

Question 14

A survey finds that 60% of people prefer tea, and 40% prefer coffee. If a person is selected at random, what is the probability that they do NOT prefer tea?

Accepted Answer

$$P(E') = 1 - 0.6 = 0.4$$

Question 15

In a genetics experiment, the probability of a plant having red flowers is 0.25 and the probability of having tall stems is 0.4. If these traits are independent, what is the probability that a plant has both red flowers and tall stems?

Accepted Answer

$$P(E) = 0.25 	imes 0.4 = 0.1$$

Question 16

A school has 100 students: 60 play soccer, 30 play basketball, and 10 play both. What is the probability that a randomly selected student plays soccer or basketball?

Accepted Answer

$$P(E) = \frac{60 + 30 - 10}{100} = \frac{80}{100} = 0.8$$

Question 17

Which formula is used to calculate the probability of an event using the classical method?

Accepted Answer

$$P(E) = \frac{	ext{number of ways E can occur}}{	ext{number of possible outcomes}}$$

Question 18

If two events A and B are independent, which equation must be true?

Accepted Answer

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

Question 19

A fair coin is flipped three times. What is the probability of getting at least one tail?

Accepted Answer

$$P(E) = 1 - \frac{1}{8} = \frac{7}{8}$$

Probability Rules and Concepts (Chapter 5, Section 5.1)

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