Question

A shipment of 5 computers contains 2 that are slightly defective, is a retailer receives three of there coputers at random , list the element be the elements of the saple space 5 using the letter D and N for defective and none defective computers respectively. to each saple point assign a value of X of the random variable X representing which is slightly defective?

Answer 1

Answer on Question #78402 – Math – Statistics and Probability

QUESTION

A shipment of 5 computers contains 2 that are slightly defective, is a retailer receives three of there computers at random, list the element be the elements of the sample space 5 using the letter D and N for defective and none defective computers respectively. to each sample point assign a value of X of the random variable X representing which is slightly defective?

SOLUTION

3N, 0D:

X=0

$$P(3N, 0D) = C_K^k \cdot \frac{C_{N-K}^{n-k}}{C_N^n} = C_3^3 \cdot \frac{C_2^0}{C_5^3} = 1 \cdot \frac{1}{10} = 0.1$$

2N, 1D:

X=1

$$P(2N, 1D) = C_K^k \cdot \frac{C_{N-K}^{n-k}}{C_N^n} = C_3^2 \cdot \frac{C_2^1}{C_5^3} = 3 \cdot \frac{2}{10} = 0.6$$

1N, 2D:

X=2

$$P(1N, 2D) = C_K^k \cdot \frac{C_{N-K}^{n-k}}{C_N^n} = C_3^1 \cdot \frac{C_2^2}{C_5^3} = 3 \cdot \frac{1}{10} = 0.3$$ $$C_K^k = \frac{K!}{k! (K - k)!}$$

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