Question

Three cooks Mohsin, Khurram, and Shahidbake a special kind of cake. In the restaurant where they work, Mohsin, bakes 55 percent of these cakes, Khurrambakes 25 percent and Shahidbakes 20 percent and with respective probabilities of 0.03, 0.02 and 0.05 they fail to rise. A cake is selected and fails to rise what is probability that it was backed by cook Khurram.

Answer 1

We denote by $A$ the event: the cake fails to rise, and by $B$ the event: the cake was baked by Khurram. The aim is to find $P(B|A)$ . Using (https://en.wikipedia.org/wiki/Conditional_probability) we have:

$P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{0.25\cdot0.02}{0.55\cdot0.03+0.25\cdot0.02+0.2\cdot0.05}=0.1587$ (rounded to 4 decimal places)

Answer:0.1587