A car parts company provides car products from a warehouse. At any given time, t

Question

A car parts company provides car products from a warehouse. At any given time, the proportion of "bad" gaskets made by Brand "X" is 0.1. There are 50 Brand "X" gaskets in stock.

a) An order has come in from 5 different dealers for one gasket each. What is the probability that 3 of the orders will ship a bad gasket?

b) Brand "Y" is now competing with Brand "X", and they are being sold along side eachother from the same warehouse. A set of 6 gaskets are being shipped out, and you happen to know that 4 of those gaskets are Brand "X", while the other two are Brand "Y". Brand "Y" does not have the same "bad" rate as Brand "X" (note: the rate of Brand "Y" is not needed to solve the problem.) What is the probability that the shipment of gaskets contains 1 Brand "X" gasket that is bad?

Explanation / Answer

Answer to part a)

P = 0.1

N = 5

X = 3

.

Binomial probability formula = nCx * p^x * (1-p)^(n-x)

P = 5C3 * (0.1)^3 * (0.99)^2

P = 10 * 0.001 * 0.9801

P = 0.009801

.

Answer to part b)

There are 4 brand x , so n = 4

And x = 1

P = 0.1

.

Binomial probability formula = nCx * p^x * (1-p)^(n-x)

P = 4C1 * (0.1)^1 * (0.99)^3

P = 4 * 0.1 * 0.970299

P = 0.3881196

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