A probability problem by Saksham Jain

The probability that a single transformer is defective is $0.02$ and the probability that it is not defective is $0.98$ .

• The probability that there are no defective transformers in the order is $P_0 = 0.98^{50}$ -- all fifty must not be defective
• The probability that there is precisely one defective transformer in the order is $P_1 = 50\times0.02\times0.98^{49}$ -- there must be one defective transformer and 49 functioning transformer, and there are 50 possibilities for which one is defective.
• The probability that there are two or more defective transformers is simply the probability that there are not 0 or 1 defective transformers. So it is $\begin{aligned} P_{\geq 2} &= 1-(P_0+P_1) \\ &= 1-(0.98^{50} + 50\times0.02\times0.98^{49}) \\ &\approx \boxed{0.26423} \end{aligned}$

Let x= number of defective transformers found in the 50 transformers So

P(order rejected) = 1 - P(x=1) - P(x=2)
= 1 - {(0.98)^50} - 50(0.02){(0.98)^49} =0.26422