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Question
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are exactly 4 defectives
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Solution
Probability of getting a defective item
p = `5/100 = 1/20`
q = 1 – p
⇒ q = `1 - 1/20`
= `(20 - 1)/20`
q = `19/20` and n = 10
In binomial distribution
P(X = x) = nCxpxqn-x
Here (X = x)= `10"C"_x (1/20)^x (19/20)(10 - x)`
p(extactly 4 defectives) = p(X = 4)
= `10"c"_4 (1/20)^4 (9/20)^(10- 4)`
= `(10 xx 9 xx 8 xx 7)/(1 xx 2 xx 3 xx 4) xx (1/20)^4 (129/20)^6`
= `210 xx (19)^6/(20)^10`
= `(210 xx 4.648 xx 10^7)/(1.023 xx 10^3)`
= `(210 xx 4.648)/(1.023 xx 10^6)`
= `(210 xx 4.648)/1023000`
= `976.08/1023000`
= 0.000954
Let x = (19)6
log x = 6 log 19
= 6 × 1.2788
log x = 7.66728
Anti log (7.66728)
x = 4.648 × 107
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