Question

Question: Refer to Exercise 3.35. Use the same event definitions to do the following exercises.

a. Write the event that the outcome is "On" and "High" as an intersection of two events.

b. Write the event that the outcome is "Low" or "Medium" as the complement of an event.

Short answer

1. 15
2. 65

Step-by-step solution

Identify the probability of the event "On and high"

The probability of an event occurring is defined by possibility. There are several real-life scenarios in which we must forecast the outcome of an occurrence. We may be one of those or uncertain about the outcome of an event.

In this case, the event with the outcome "On and high" is expressed as follows:

$\mathbf{On}\mathbf{\cap }\mathbf{high}$

The probability of this occurrence is,

$\mathbf{P}\mathbf{(}\mathbf{On}\mathbf{\cap }\mathbf{high}\mathbf{)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$

Hence, the required probability is 0.05.

Identify the probability of the event "Low and medium" as a complement to an event

The event with the consequence "Low" or "Medium" might be written as a complement to another event, such as,

${\mathbf{\left(}\mathbf{High}\mathbf{\right)}}^{\mathbf{c}}\mathbf{=}\mathbf{low}\mathbf{\cup }\mathbf{medium}$

The probability of this occurrence is,

$$\begin{gathered} \mathbf{P}{\left(\mathrm{High}\right)}^{\mathbf{c}}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{P}\mathbf{\left(}\mathbf{High}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{08} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{92} \end{gathered}$$

Hence, the required probability is 0.92.