SOLUTION: 70% of the people who tried a hamburger liked it. 8 customers bought it for the first time. find the probability that at exactly 5 people like the hamburger

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Question 349551: 70% of the people who tried a hamburger liked it. 8 customers bought it for the first time.
find the probability that at exactly 5 people like the hamburger

Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
a) This is a contradiction : if 5 out of 8 liked, this is 5/8=62.5% which is not 70% who normally should like

b) If the prob. somebody eating an hamburger like it is 0.7, then :
choosing 5 people out of 8 gives : C(8,5)=8*7*6/(3*2)=8*7=56 possibilities.

prob that these 5 like the ham. : 0.7^5
prob that the 3 remaining don't : 0.3^3

hence P=56*.7^5*0.3^3=0.254