An instrument has two units; first functions with probability 0.9, second with 0.8.

Question

An instrument has two units; first functions with probability 0.9, second with 0.8. Instrument fails to operate. If probability only first failed and second functioning is $P$, find $98P$.

Answer: 28

Accepted Answer

$$P = \frac{P(\overline A)P(B)}{P(\overline A)P(B)+P(A)P(\overline B)+P(\overline A)P(\overline B)} = \frac{0.1\times0.8}{0.9\times0.2+0.1\times0.8+0.1\times0.2} = \frac{0.08}{0.28}=\frac{8}{28}$$

$$98P = 98\times\frac{8}{28}=28$$

Solutions · 1