4.2: Probability and Events

Question 1

What is an event in the context of probability?

Answer 1

An event is a set of one or more sample space outcomes.

Question 2

How do you find the probability of an event?

Answer 2

The probability of an event is the sum of the probabilities of the sample space outcomes that correspond to the event.

Question 3

What is the probability that at least five spots will show on the upward face of a fair die?

Answer 3

1/3 (since P(5) + P(6) = 1/6 + 1/6 = 1/3).

Question 4

In the experiment of having two children, what is the sample space?

Answer 4

The sample space is BB, BG, GB, GG, representing all combinations of two children being boys (B) or girls (G).

Question 5

If a couple plans to have two children, what is the probability they will have two boys?

Answer 5

1/4 (since P(BB) = 1/4).

Question 6

What is the probability of having one boy and one girl?

Answer 6

1/2 (since P(BG) + P(GB) = 1/4 + 1/4 = 1/2).

Question 7

What is the probability of having at least one girl?

Answer 7

3/4 (since P(BG) + P(GB) + P(GG) = 1/4 + 1/4 + 1/4 = 3/4).

Question 8

How is the tree diagram used in the context of probability?

Answer 8

A tree diagram is used to depict the sample space of an experiment, showing all possible outcomes at the ends of its branches.

Question 9

What is the probability that a student will answer all questions correctly in a 3-question true/false quiz if guessing?

Answer 9

1/8 (since P(CCC) = 1/8).

Question 10

What is the probability that the student will get exactly two questions correct if guessing?

Answer 10

What is the probability that the student will get exactly two questions correct if guessing?
A: 3/8 (since P(CCI) + P(CIC) + P(ICC) = 1/8 + 1/8 + 1/8).

Question 11

What is the probability that the student will get exactly one question correct if guessing?

Answer 11

3/8 (since P(CII) + P(ICI) + P(IIC) = 1/8 + 1/8 + 1/8).

Question 12

What is the general method for computing the probability of an event when all sample space outcomes are equally likely?

Answer 12

The probability is the ratio of the number of sample space outcomes that correspond to the event to the total number of sample space outcomes.

Question 13

Why can’t the rule of equally likely outcomes always be used to compute probabilities?

Answer 13

The rule can only be used when all sample space outcomes are equally likely; otherwise, it may give an incorrect probability.