a math club is researching a golf tournament fund - raiser. it will cost $1,000 to host the tournament. if…
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?\n- $800\n- $200\n$2,600\n$3,400
Answer
Explanation:
Step1: Calculate the probability of sunny weather
The probability of rain is 20% or 0.2. The probability of sunny weather $P(S)$ is $1 - 0.2=0.8$.
Step2: Calculate the net - gain in case of rain
The cost to host the tournament is $1000$. If it rains, the club loses the investment, so the net - gain $G_R=- 1000$.
Step3: Calculate the net - gain in case of sunny weather
The club collects $4500$ and has a cost of $1000$. So the net - gain $G_S = 4500 - 1000=3500$.
Step4: Calculate the expected value
The formula for expected value $E$ is $E = P(R)\times G_R+P(S)\times G_S$. Substitute the values: $E=(0.2\times(-1000))+(0.8\times3500)$. First, $0.2\times(-1000)=-200$, and $0.8\times3500 = 2800$. Then $E=-200 + 2800=2600$.
Answer:
$2600$ (corresponding to the option $$2,600$)