Chapter 4, Problem 1PS

Three coins are tossed.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. What is the complement of a head on the first toss?

d. what does the sample space consist of?

To determine

Determine an example of a simple event when three coins are tossed.

Answer to Problem 1PS

Simple events are tossing the heads or tossing a tail

Explanation of Solution

A simple event is an event that has only one characteristic, that is, it contains the outcomes that cannot be further subdivided.

An example of a simple event, when a coin is tossed, is either getting a head or getting a tail. These outcomes represent one characteristics, and it cannot be further subdivided.

To determine

Determine an example of a joint event when three coins are tossed.

Answer to Problem 1PS

Joint events are tossing three heads, tossing three tail etcetera.

Explanation of Solution

Joint Event is an event that has two or more characteristics. Joint probability is the likelihood of more than one event occurring at the same time.

An example of a joint event can be simultaneously tossing three heads $\left\{\text{HHH}\right\}$ ,or a tail followed by two heads $\left\{\text{THH}\right\}$ or a head followed by two tails $\left\{\text{HTT}\right\}$ or simultaneously tossing three tails $\left\{\text{TTT}\right\}$ . All these events have more than one characteristic, and it can be further subdivided.

To determine

Determine the complement of an event ‘head on the first toss’.

Answer to Problem 1PS

The complement of head is getting a tail.

Explanation of Solution

Complement is the subset of outcomes that are not a part of the event.

When a coin is tossed twice, there are two possible outcomes which are getting a head or getting a tail. Both these events are mutually exclusive and exhaustive events.

Therefore, if the head comes up, tail can’t and vice versa. So, the complement of a head on the first toss will be tail coming on the first toss.

To determine

Determine the sample space on tossing three coins.

Explanation of Solution

Sample Space is the set of all possible outcomes. So, the sample space of tossing three coins will consist of 8 outcomes which are: $\left\{\text{HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}\right\}$