The probability that a randomly selected person has high blo

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.5. The probability that a randomly selected person has high blood pressure and is a runner is 0.1. Find the probability that a randomly selected person is a runner, given that he has high blood pressure.

Solution

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4

the probability that a randomly selected person is a runner (the event R) is P(R) = 0.5

The probability that a randomly selected person has high blood pressure and is a runner is 0.1

which means P[H and R]=0.1

we need to find the probability that a randomly selected person is a runner, given that he has high blood pressure.

which means we need to find P[R|H]

now P[R|H]=P[R and H]/P[H]      [by the definition of conditional probability]

now P[R and H]=P[H and R]=0.1

and P[H]=0.4

so P[R|H]=0.1/0.4=1/4=0.25

so the the probability that a randomly selected person is a runner, given that he has high blood pressure is 0.25 [answer]