SOLUTION: if 7 mangoes are chosen at random from 10 mangoes of which 3 are rotten, what is the probability that exactly one is not rotten and the probability that at least one is rotten?

Question 994679: if 7 mangoes are chosen at random from 10 mangoes of which 3 are rotten, what is the probability that exactly one is not rotten and the probability that at least one is rotten?
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
probability of one being not rotten is 0.7.
Exactly 1 is 7(0.7)^1(0.3)^6, the 7 being the number of ways it can be chosen, first, second, third, fourth, fifth, sixth, or seventh.
=0.00357
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for at least one is rotten: Probability none is rotten and subtract that from 1. That is easier than calculating 1,2,3,4,5,6,7.
The probability that none is rotten is 0.7^7=0.0824
The probability that at least one is rotten is the complement, or 0.918
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if 7 mangoes are chosen at random from 10 mangoes of which 3 are rotten, what is the probability that exactly one is not rotten
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Binomial Problem with n = 7 and p(rotten) = 3/10; p(not rotten) = 7/10
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P(x = 1 not rotten) = 7C1*(7/10)*(3/10)^6 = binompdf(7,7/10,1) = 0.0036
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and the probability that at least one is rotten?
P(1<= x <= 7) = 1 - P(x = 0 rotten) = 1 - (7/10)^7 = 0.9177

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Cheers,
Stan H.

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