Question

For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event

Answer 1

The experiments consist of rolling a number cube three times and is recorded whether the number was even "E" or odd "O".

Each outcome of the experiment is represented by the three results obtained, for example EOE indicates that the first number was even, the second was odd, and the third was even.

Each outcome is considered to have the same probability and a total of 8 outcomes are listed on the table, this means that the probability of each outcome is 1/8.

Event A: "Exactly one odd number"

This event occurs when only one odd number was registered, this means that out of the 8 outcomes listed, only those with one "O" will correspond to this event:

There are three events that meet the condition for event A.

To calculate the probability of this event, you have to divide the number of successes by the total number of outcomes:

`\begin{gathered} P(A)=\frac{nºsuccesses}{total\text{ }outcomes} \\ P(A)=(3)/(8) \end{gathered}`

The probability of event A is 3/8.

Event B: "An even number on the first roll"

To determine the probability of event B, the first step is to identify all outcomes that meet this condition. These outcomes will represent the successes of event B.

There are 4 outcomes that registered an even number on the first roll, you can calculate the probability of this event as follows:

`\begin{gathered} P(B)=\frac{nºsuccesses}{total\text{ }outcomes} \\ P(B)=(4)/(8) \\ P(B)=(1)/(2) \end{gathered}`

The probability of event B is 1/2.

Event C: "An even number on both, the first and the last roll"

First, identify the outcomes that registered an even number (E) on the first and the last roll:

There are 2 outcomes that meet the condition stated for event C. You can calculate the probability of this event as follows:

`\begin{gathered} P(C)=\frac{nºsuccesses}{total\text{ }outcomes} \\ P(C)=(2)/(8) \\ P(C)=(1)/(4) \end{gathered}`

The probability of C is 1/4.