Question

The probability that Jacqueline will be elected to the students' council is o.6, and the probability that she will be selected to represent her school in a public-speaking contest is 0.75. The probability of Jacqueline achieving both of these goals is 0.5. Answer the questions below:1. The two evens are mutually exclusive. True or False2. The events are not independent. True or False3. What is the probability that Jacqueline is either elected to the student' council or picked for the public-speaking contest? Round you answer to two decimal place

Answer 1

Recall that two events are mutually exclusive if they cannot happen at the same time. In the given problem we are given that the probability of both events occurring is 0.5 therefore, the events are not mutually exclusive.

Now, two events are independent if one event happening does not affect the probability of the other, in the given problem the events don't affect each other, therefore, the events are independent.

Finally, to determine the probability of either event happening, we will use the following formula for not mutually exclusive events:

`P(A\cup B)=P(A)+P(B)-P(A\cap B).`

We know that:

`\begin{gathered} P(A)=0.6, \\ P(B)=0.75, \\ P(A\cap B)=0.5. \end{gathered}`

Therefore:

`P(A\cup B)=0.6+0.75-0.5=0.85.`

Answer:

1) False.

2) False.

3) 0.85.