Question

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect $4,500 from the participants. If the chance of rain is 20%, what is the expected value for the tournament? @DanJS

Answer 1

@DanJS

Answer 2

Expected value: \[
E[X] =\mu =\sum_{i} x_i\cdot \Pr(X=x_i)
\]

Answer 3

In this case, we have two \(i\) values.
\(i=1\) is the case that it rains.
\(i=2\) is the case that it doesn't rain.

Answer 4

Here are the earnings:\[
x_1= -$1000\\
x_2 = $4500-$1000 = $3500
\]

Answer 5

Here are the probabilities: \[
\Pr(X=x_1) = 0.20\\
\Pr(X=x_2) = 1-0.20 = 0.80
\]

Answer 6

Therefore... \[
E[X] = 0.20\cdot (-$1000) + 0.80\cdot ($3500)
\]

Answer 7

2600 and 3400 are the only answers that are positive

Answer 8

All that remains is to multiply and add.

Answer 9

2600
thank you!

Answer 10

But do you understand how I did it...

Answer 11

I remembered the formula, and that you took the two probabilities of the occurrences and multiplied them