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?

• $800
• $200

$2,600
$3,400

Explanation:

Step1: Define outcomes & probabilities

Rain: Probability $P_r = 0.2$, Net value $V_r = -\$1000$
Sunny: Probability $P_s = 1-0.2=0.8$, Net value $V_s = \$4500 - \$1000 = \$3500$

Step2: Calculate expected value

Expected Value $E = P_rV_r + P_sV_s$
$E = (0.2 \times -1000) + (0.8 \times 3500)$

Step3: Compute each term

$0.2 \times -1000 = -200$
$0.8 \times 3500 = 2800$

Step4: Sum the terms

$E = -200 + 2800 = 2600$

Answer:

$2,600$