Question

1. outdoor regatta a producer plans an outdoor regatta for may 3. the cost of the regatta is $8000. this includes advertising, security, printing tickets, entertainment, etc. the producer plans to make $15,000 profit if all goes well. however, if it rains, the regatta will have to be canceled. according to the weather report, the probability of rain is 0.3. find the producer’s expected profit.

Explanation:

Step1: Determine profit in each scenario

• If it does not rain (probability \( 1 - 0.3 = 0.7 \)): The profit is \( \$15000 \) (since cost is already accounted for in the profit calculation as the producer plans to make this profit after covering costs).
• If it rains (probability \( 0.3 \)): The regatta is canceled, so the producer will lose the cost of \( \$8000 \), so the profit is \( -\$8000 \) (a loss of \( \$8000 \)).

Step2: Calculate expected profit

The formula for expected value \( E(X) \) is \( E(X)=\sum_{i} x_i P(x_i) \), where \( x_i \) are the possible values and \( P(x_i) \) are their corresponding probabilities.

So, \( E(\text{Profit})=(15000\times0.7)+(- 8000\times0.3) \)

First, calculate \( 15000\times0.7 = 10500 \)

Then, calculate \( - 8000\times0.3=-2400 \)

Now, add these two results: \( 10500-2400 = 8100 \)

Answer:

The producer's expected profit is \(\$8100\)