Question

for an outdoor concert by the city orchestra, concert organizers estimate that 12,000 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 80% chance of rain. determine the expected number of people who will attend this concert

Answer 1

The probability that it rains on the day of the concert is: 80% or 0.8

Thus, the probability that it does not rain on the day of the concert is: 20% or 0.2.

To solve this problem we use the expected value formula:

$E=\sum ^{\square}_{\square}x\cdot p(x)$

Where x is the number of people who will attend on each scenario, and p(x) is the probability for such scenario.

In this case, we can interpret the formula as follows:

Expected number of people = (number of expected attendees if it does not rain*probability that it does not rain) + (number of expected attendees if it rains*probability that it rains)

Substituting the known values:

$\text{Expected number of people=12,000}\cdot0.2+7000\cdot0.8$

The result is:

$\begin{gathered} \text{Expected number of people=}2,400+5,600 \\ \text{Expected number of people=}8,000 \end{gathered}$

Answer: 8,000