SOLUTION: Please help me with the following problem. Thank you. In a factory, products are packed into boxes. Every box has 10 products, 7 of them are of type A(good product). The custome

Question 252362: Please help me with the following problem. Thank you.
In a factory, products are packed into boxes. Every box has 10 products, 7 of them are of type A(good product). The customer check the products as follows: randomly take 3 products from a box, if all of them are of type A then that box is accepted; otherwise that box is refused. Assume that there are 100 boxes inspected. Find:
a)The probability that there are 25 boxes accepted.
b)The probability that there are less than 30 boxes accepted.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a factory, products are packed into boxes. Every box has 10 products, 7 of them are of type A(good product). The customer check the products as follows: randomly take 3 products from a box, if all of them are of type A then that box is accepted; otherwise that box is refused. Assume that there are 100 boxes inspected.
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Probability that a random box is accepted:
P(accept) = 7C3/10C3 = 35/120 = 7/24
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Find:
a)The probability that there are 25 boxes accepted.
A binomial Problem with n = 100, p = 7/24, x = 25
Ans: binompdf(100,7/24,25) = 0.0595...
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b)The probability that there are less than 30 boxes accepted.
Ans: binomcdf(100,7/24,29) = 0.5353..
Cheers,
Stan H.

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