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.

The expected number of people who will attend the concert is 8500 and this can be determined by using the given data.

Given :

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, meteorologists predict a 30% chance of rain.

Given that the probability of having rain is 30% that is 0.3.

So, the probability of not having rain is 1 - 0.3 = 0.7.

Now, the expected number of people who will attend the concert will be:

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

= 1500 + 7000

= 8500

So, the expected number of people who will attend the concert is 8500.

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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

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