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

Answer 1

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) = nC_xp^xq^n-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