Question

2% of the blades manufactured by a firm are defective. Blades are supplied in packets of 5 each. What is the probability that randomly selected packet will have atleast one defective?

Answer 1

Let x denote the number of defective blades is a Binomial variate with the parameters n = 5. 

p = p[blade is defective] 

= 2% = 0.02, 

∴ q = 0.98. 

The p.m.f is –

p(x) = nc_xp^xq^{n – x} ; x = 0,1,2, …… n

= 5c_x (0.02)^x (0.98)^{5 – x} ; x = 0,1,2, …….. 5

p (packet has atleast one defective) = p(x ≥ 1)

= 1 – p (packet has no defectives)

= 1 – p (x = 0)

= 1 – 5c₀ (0.02)⁰ (0.98)^5-0

= 1 – 0.9039 = 0.0961

[Note: This problem can also be solved by poisson distribution.]