Question

A batch of fifty radio sets was purchased from three different companies A, B and C. Eighteen of them were manufactured by A, twenty of them by B and the rest were manufactured by C.
The companies $A$ and $C$ produce excellent quality radio sets with probability equal to 0.9 ; $B$ produces the same with the probability equal to 0.6 .
If the probability of the event that the excellent quality radio set chosen at random is manufactured by the company $B$ is expressed as $\frac{p}{q}$, find the least value of $(p+q)$.

Answer 1

Answer: 17

Let A, B, C be the events that the radio set chosen, is manufactured by the companies A, B
and C respectively. Let E be the event that the radio set is of excellent quality

$\text{ Thus }P(A)=\frac{18}{50};P(B)=\frac{20}{50};P(C)=\frac{12}{50}$
$P(E/A)=0.9;P(E/B)=0.6;P(E/C)=0.9$
$\therefore P(E)=P(A)P(E/A)+P(B)P(E/B)+P(C)P(E/C)=\frac{39}{50}$
required probability $=P(B/E)=\frac{P(B)P(E/B)}{P(E)}=\frac{4}{13}$