12. outdoor regatta a producer plans an outdoor regatta for may 3. the cost of the regatta is $8000. this…

12. 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.

12. 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.

Answer

Explanation:

Step1: Define the two scenarios

  • Scenario 1: No rain (probability ( P(\text{no rain}) = 1 - 0.3 = 0.7 )). In this case, the profit is ( $15000 ).
  • Scenario 2: Rain (probability ( P(\text{rain}) = 0.3 )). In this case, the regatta is canceled, so the profit is ( -$8000 ) (since the cost of $8000 is incurred with no revenue).

Step2: Use the formula for expected value

The formula for the expected value ( E(X) ) of a discrete random variable is ( E(X) = \sum [x_i \cdot P(x_i)] ), where ( x_i ) are the possible values and ( P(x_i) ) are their corresponding probabilities.

For this problem: [ \begin{align*} E(\text{Profit})&=(15000\times0.7)+(-8000\times0.3)\ &= 10500 - 2400\ &= 8100 \end{align*} ]

Answer:

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