Can u please show the steps not just the solution So I can b

Can u please show the steps not just the solution. So I can better understand the problem.

A box contains 15 defective and 35 flawless electronic components.A quality control officer randomly sample 10.Let X denote the number of defective components in his sample.

a) Find the distribution of X

b) E(X)

Solution

a)

If n = sample size

N = population size

K = number of successes in the population,

We have a hypergeometric distribution here. If x denotes the number of defective components,

P(x) = C(K,x) C(N-K, n-x) / [C(N, n)]

P(x) = C(15,x) C(35, 10-x) / [C(50, 10)]

We C(n, r) = combinations of n taken r at a time.

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b)

If n = sample size

N = population size

K = number of successes in the population,

E(x) = n (K/N) = 10*(15/50) = 3 [ANSWER]