Question

In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.

Answer 1

Let x% of students pass in both Physics and Mathematics

Students pass in Physics = 70% ⇒ P (P) = `(70)/(100)`

Students pass in Mathematics = 75% ⇒ P (M) = `(75)/(100)`

Students fail in both = 10%

Now students pass in physics only + students pass in mathematics only + students pass in both physics and mathematics = 90%

⇒ 70% - x + x + 75% - x = 90%

x = 55% ⇒ P (M ∩ P) = `(55)/(100)`

(i)

P ( Passes in Physics and Mathematics) = `(55)/(100) = (11)/(20)`

(ii)

P (M/P) = `(P (M ∩ P))/(P(P)`

= `((55)/(100))/(70/(100))`

= `(55)/(70) = (11)/(14)`

(iii)

`P(P/M) = (P(M ∩ P))/(P(M))`

`(55/100)/(75/100)`

= `55/75 = 11/15`