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.

the law, public safety, corrections, and security cluster prepares people for careers in planning, managing, and providing legal, public safety, protective services and homeland security, including professional and technical support services.