5. There are two groups of subjects one of which contains 5 science subjects and 3 engineering subjects and the other consists of 3 science and 5 engineering subjects. An unbiased die is cast. If the number 3 or number 5 turns up, a subject is selected at random from the first group, otherwise the subject is selected at random from the second group. Find the probability that an engineering subject is selected ultimately.

Question

5.	There are two groups of subjects one of which contains 5 science subjects and 3 engineering subjects and the other consists of 3 science and 5 engineering subjects. An unbiased die is cast. If the number 3 or number 5 turns up, a subject is selected at random from the first group, otherwise the subject is selected at random from the second group. Find the probability that an engineering subject is selected ultimately.

Reiny · Answer

Engineering -- E
Science ------ S

Prob (E is picked from 1st group) = 3/8
prob(E is picked from the 2nd group) = 5/8

first picking is determined by a die toss of 3 or 5
which has a prob of 2/6 or 1/3
2nd picking is determined by any other die toss
which is 2/3

prob of your stated event
= (1/3)(3/8) + (2/3)(5/8)
= 3/24 + 10/24
= 13/24