For an outdoor concert by the city orchestra, concert organizers estimate that 16 comma 000 people will attend if it is not rai
ning. If it is raining, concert organizers estimate that 7000 people will attend. On the day of the concert, meteorologists predict a 30% chance of rain. Determine the expected number of people who will attend this concert.
Multiply the attendance figures with their corresponding probabilities
if it rains, then 7000*P(A) = 7000*0.30 = 2100
if it doesn't rain, then 16000*P(B) = 16000*0.70 = 11200
Add up the results: 2100+11200 = 13300
This is the expected value. This is basically the average based on the probabilities. The average is more tilted toward the higher end of the spectrum (closer to 16000 than it is to 7000) because there is a higher chance that it does not rain.
