In their recent exams 75% of a group of 4th year medical students passed pediatrics, 60% passed obstetrics and 50% passed both.
a) Given that a student passed pediatrics what is the probability that the student also passed obstetrics?
Let A be the probability that a student passed pediatrics.
Let B be the probability that a student passed obstetrics.
A student passing both pediatrics and obstetrics corresponds to the event that A intersection B (`A cap B` ) occurs. The probability that the student passed obstetrics given that the student passed pediatrics is denoted by `P(B | A).`
This is a conditional probability. The formula for this is:
`P(B|A) = (P(A cap B))/(P(A))`
This is like restricting the sample space only to A since it we know that is has already occurred.
From the problem, we know that:
P(A) = 75%
P(B) = 60%
`P(A cap B)` =50%
`P(B|A) = (0.50)/(0.75) = 0.67`
The probability that a student passed obstetrics given that he passed pediatrics is 66.67%.