For an outdoor concert by the city orchestra, concert organizers estimate that 10,000 people will attend if it's not raining. If it is raining, concert organizers estimate 5000 people will attend. On the day of the concert meteorologist predict a 30% chance of rain. Determine the expected number of people who will attend the concert.

Question

Mathematics

Quinton Mayo

28 August, 23:28

For an outdoor concert by the city orchestra, concert organizers estimate that 10,000 people will attend if it's not raining. If it is raining, concert organizers estimate 5000 people will attend. On the day of the concert meteorologist predict a 30% chance of rain. Determine the expected number of people who will attend the concert.

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Amelia Wiggins · Answer 1

The number of expected people at the concert is 8,500 people

Step-by-step explanation:

In this question, we are asked to determine the expected number of people that will attend a concert if we are given the probabilities that it will rain and it will not rain.

We proceed as follows;

The probability that it will rain is 30% or 0:3

The probability that it will not rain would be 1 - 0.3 = 0.7

Now, we proceed to calculate the number of people that will attend by multiplying the probabilities by the expected number of people when it rains and when it does not rain.

Mathematically this is;

Number of expected guests = (probability of not raining * number of expected guests when it does not rain) + (probability of raining * number of expected guests when it rains)

Let's plug values;

Number of expected guests = (0.3 * 5,000) + (0.7 * 10,000) = 1,500 + 7,000 = 8,500 people