SOLUTION: A study done at a University shows that 80% of College students prefer pizza over chicken nuggets for lunch. A random sample of 8 people is chosen. (a) Calculate the probabili

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Question 1147534: A study done at a University shows that 80% of College students prefer pizza over chicken nuggets for lunch. A random sample of 8 people is chosen.

(a) Calculate the probability that no more than 4 of them will eat pizza for lunch.
(b) Calculate the probability that exactly 2 of them will eat chicken nuggets for lunch.

(c) Calculate the probability that none of them will eat pizza for lunch.

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
(a) Calculate the probability that no more than 4 of them will eat pizza for lunch.

Probability exactly four will eat pizza: %280.80%29%5E4+%2A+%280.20%29%5E4+%2A+%288%21%2F%284%21%2A4%21%29%29 = 0.0459
Probability exactly three will eat pizza: %280.80%29%5E3+%2A+%280.20%29%5E5+%2A+%288%21%2F%283%21%2A5%21%29%29 = 0.0092
Probability exactly two will eat pizza: %280.80%29%5E2+%2A+%280.20%29%5E6+%2A+%288%21%2F%282%21%2A6%21%29%29 = 0.0011
Probability exactly one will eat pizza: %280.80%29%5E1+%2A+%280.20%29%5E7+%2A+%288%21%2F%281%21%2A7%21%29%29 = 0.0001
Probability none will eat pizza: %280.20%29%5E8 = 0.000003

Probability no more than four will eat pizza for lunch: 0.0459+%2B+0.0092+%2B+0.0011+%2B+0.0001+%2B+0.000003 = 0.0563 (rounded)

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(b) Calculate the probability that exactly 2 of them will eat chicken nuggets for lunch.

%280.20%29%5E2+%2A+%280.80%29%5E6+%2A+%288%21%2F%282%21%2A6%21%29%29 = 0.2936

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(c) Calculate the probability that none of them will eat pizza for lunch.

We already calculated this in Part A.

%280.20%29%5E8 = 0.000003