Question

The probability that a randomly chosen male has a blood circulation problem is 0.25. Males who have a blood circulation problem are twice as likely to be smokers as those who do not have a blood circulation problem. Calculate the probability that a male has a blood circulation problem, given that he is a smoker.

Answer 1

The probability that a male has a blood circulation problem and he is a smoker is 0.4.

Explanation:

We have given,

The probability that a randomly chosen male has a blood circulation problem is 0.2.

P(Circulation) = .25

P(smoker | circulation) = 2 × P(smoker | not circulation)

Let P(smoker | not circulation) = x

Therefore P(smoker | circulation) = 2x

Let smoker = S, circulation = C

`P(C\ |\ S)=\frac P(S\ \ C)* P(C) + P(S\`

`P(C\ |\ S)=\frac {2x * 0.25}{[2x * 0.25 + x * 0.75]} = \frac {0.5x}{(0.5x + 0.75x)} \\\\\\P(C\ |\ S)= \frac {0.5x}{1.25x} = 0.4`

Thus, the probability that a male has a blood circulation problem, given that he is a smoker is 0.4.