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...

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?

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mvcdc | Student, Graduate | (Level 2) Associate Educator

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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%

Hence, 

`P(B|A) = (0.50)/(0.75) = 0.67`

The probability that a student passed obstetrics given that he passed pediatrics is 66.67%.

Sources:

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