Question

For an outdoor concert by the city​ orchestra, concert organizers estimate that 16 comma 000 people will attend if it is not raining. 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.

Answer 1

Answer:  13300

========================================

Work Shown:

A = event that it rains

B = event that it does not rain

P(A) = 0.30

P(B) = 1-P(A) = 1-0.30 = 0.70

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.