40% of the buttons manufactured by a firm are found to be defective. I

1.	40% of the buttons manufactured by a firm are found to be defective. In a random sample of six buttons, find the probability of getting.(i) exactly 4 defective buttons (ii) more than one defective button.
Answer» Let X be the number of buttons manufactured is a Binomial. Variate with parameters n = 6 and p = 40% = 0.4, so q = 1 – p = 0.6. Then the probability mass function is: p (x) = ⁿC_x p^x q^n-x= 0, 1, 2 ……. n. = ⁶C^x (0.4)^x (0.6)^6-x ; x = 0, 1, 2 6. (i) P(exactly 4 defective buttons) = p(x = 4) = ⁶C₄ (0.4)⁴ (0.6)^6-4 = 15 × 0.0256 × 0.36 = 0.1382 (ii) P(more than 1 defective button) =p(x > 1) = 1 -p(x = 0) = ⁶C₀ (0.4)⁰ (0.6)^6-0 = 1.1. 0.466 = 0.0466.

40% of the buttons manufactured by a firm are found to be defective. In a random sample of six buttons, find the probability of getting.(i) exactly 4 defective buttons (ii) more than one defective button.

Answer»

Let X be the number of buttons manufactured is a Binomial.

Variate with parameters n = 6 and p = 40% = 0.4, so q = 1 – p = 0.6.

Then the probability mass function is:

p (x) = ⁿC_x p^x q^n-x= 0, 1, 2 ……. n.

= ⁶C^x (0.4)^x (0.6)^6-x ; x = 0, 1, 2 6.

(i) P(exactly 4 defective buttons) = p(x = 4)

= ⁶C₄ (0.4)⁴ (0.6)^6-4 = 15 × 0.0256 × 0.36

= 0.1382

(ii) P(more than 1 defective button)

=p(x > 1) = 1 -p(x = 0)

= ⁶C₀ (0.4)⁰ (0.6)^6-0 = 1.1. 0.466

= 0.0466.

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40% of the buttons manufactured by a firm are found to be defective. In a random sample of six buttons, find the probability of getting.(i) exactly 4 defective buttons (ii) more than one defective button.

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