In an examination 30% of the students failed in Physics, 25% in Mathematics and 12% in both Physics and Mathematics. A student is selected at random. Find the probability that the student has failed in Physics, if it is known that he has failed in Mathematics. (ii) the student has failed at least one of the two subjects (ii) the student has passed at least one of the two subjects (iv) the student has passed in Mathematics if he failed in Physics.

Explanation

let the event of student failed in physics be P

let the event of student failed in maths be M

`P(P) = 3/10`

`P(M)= 1/4`

`P(P nn M) =3/25`

(I)`P(P/M)= (P(P nn M))/(P(M)) = (3/25)/(1/4) = 12/25`

(ii)`P(P uu M) = P(P) + P(M) -P(P nn M)`

`= 3/10 + 1/4 - 3/25 = 43/100 = 0.43`

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