Question

For an outdoor concert by the city orchestra, concert organizers estimate that 16,000 people will attend if it is not raining. If it is raining, concert organizers estimate that 6000 people will attend. On the day of the concert, meteorologists predict a40% chance of rain. Determine the expected number of people who will attend this concert.It is expected thatpeople will attend the concert.

Answer 1

The formula for calculating the expected number of people is

Ex = xPx

where

Px represents the probability of an event, x

From the information given,

when it is raining, 6000 people will attend

Probability that it will rain = 40% = 40/100 = 0.4

when it is not raining, 16,000 people will attend

Probability that it will not rain = 1 - 0.4 = 0.6

Thus,

Expected number of people who will attend this concert = (6000 * 0.4) + (16000 * 0.6) = 2400 + 9600

Expected number of people who will attend this concert = 12000