Question

Calculate the expected value to make predictions.

Niceville Community plans to invest $1,200 to host a concert. The community expects to sell tickets worth $1,600. But if it rains on the night of the concert, they won't sell any tickets, so they will lose all the money invested. The weather forecast for the day of the concert is 20% chance of rain. How much money can the community expect to make?

A. $0.65
B. $80
C. -$0.50
D. -$2.00

Answer 1

The expected value for the Niceville Community concert, considering an 80% chance of making a $400 profit and a 20% chance of losing $1,200 due to rain, is $80.

Step-by-step explanation:

To calculate the expected value for the Niceville Community concert scenario, we need to consider both outcomes: the concert happening without rain and the concert being canceled due to rain. The expected value is determined by multiplying each outcome by its probability and then adding these products together.

• If it does not rain (which has an 80% chance), the community will make a profit of $1,600 - $1,200 = $400.
• If it rains (which has a 20% chance), the community will lose $1,200, since no tickets will be sold.

The expected value (EV) can be calculated as follows:

EV = (Probability of no rain * Profit if it does not rain) + (Probability of rain * Loss if it rains)

EV = (0.80 * $400) + (0.20 * -$1,200)

EV = ($320) + (-$240)

EV = $320 - $240

EV = $80

Therefore, the community can expect to make an average of $80 from hosting the concert.

Answer 2

I believe its b not 100 percent sure.