Suppose 30% of a club are above 25 years old (M), 50% are between 21 and 25 (W) and 20% are below 21 (L). If all are exposed to a virus but only 65% of M, 82% of W and 50% of L get the virus. We select a person at random and he/she has the virus. What is the probability he/she is aged between 21 and 25?

The probability that a person selected at random has virus and is aged between 21 and 25 is 0.58.

Explanation:

let A be the event that the selected person has a virus.

let B1, B2 and B3 be the events that the selected perosn is M, W and L accordingly.

the probabilities are given by:

P (B1) = 0.3

P (B2) = 0.5

P (B3) = 0.2

P (A|B1) = 0.65

P (A|B2) = 0.82

P (A|B3) = 0.5

probability of having virus and aged between 21 and 25 is given by:

[P (B2) * P (A|B2) ]/[P (B1) * P (A|B1) + P (B2) * P (A|B2) + P (B3) * P (A|B3) ]

= [ (0.5) * (0.82) ]/[ (0.3) * (0.65) + (0.5) * (0.82) + (0.2) * (0.5) ]

= 0.58

Therefore, the probability that a person selected at random has virus and is aged between 21 and 25 is 0.58.