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On a Saturday evening, 34% of the people in Chicago go out to dinner, 18% see a movie, 13% have a party, and 35% stay home. If seven people are randomly selected, what is the probability that one eats out, three see a movie, two have a party, and one stays at home

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Answer:

The probability is 0.00493

Step-by-step explanation:

From the data in the question, probability of eating out is 34% = 0.34

Probability of seeing a movie = 18% = 0.28

Probability of having a party = 13% = 0.13

Probability of staying home = 35% = 0.35

We use the multinomial distribution format to calculate this.

The probability would thus be;

{7! ÷ (1! * 2! * 3! * 1!) } * 0.34^1 * 0.28^3 * 0.13^2 * 0.35^1 = 0.00493

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