Question

a math club is researching a golf tournament fund - raiser. it will cost $1000 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 $4500 from the participants. if the chance of rain is 20%, what is the expected value for the tournament?

• $800
• $200

$2600
$3400

Explanation:

Step1: Calculate probability of sunny

The probability of rain is 20% or 0.2. So the probability of sunny is $1 - 0.2=0.8$.

Step2: Calculate the value in case of rain

If it rains, the club loses the investment. The cost of hosting is $1000$, so the value in case of rain is $- 1000$.

Step3: Calculate the value in case of sunny

If it is sunny, the club will collect $4500$. But there is a cost of $1000$ for hosting. So the net - value in case of sunny is $4500 - 1000=3500$.

Step4: Calculate the expected value

The formula for expected value $E(X)$ is $E(X)=p_1x_1 + p_2x_2$, where $p_1$ and $p_2$ are probabilities and $x_1$ and $x_2$ are corresponding values. Here, $p_1 = 0.2$, $x_1=-1000$, $p_2 = 0.8$, and $x_2 = 3500$. So $E(X)=0.2\times(-1000)+0.8\times3500=-200 + 2800=2600$.

Answer:

$2600$