Question

A question is given to two students A and B the probabilty of A solving the question are 6 to 9 and against B solving the question are 10 to 12. if both A and B attempt solving the question, find the probability of the question being solved?. HELP

p(a)=6:9
p(b)=10:12

Answer 1

94% or `17/18`.

Explanation:

The question can be solved in one of three ways: A solves it but B doesn't, B solves it but A doesn't, and both solve it. So, let's break it down.

The probability that A solves it and B doesn't is: `6/9*2/12=12/108`.

The probability that B solves it and A doesn't is: `10/12*3/9=30/108`.

The probability that both solve it is: `6/9*10/12=60/108`.

So, the total probability that the question is solved is: `12/108+20/108+60/108=102/108`.

This can be simplified as `17/18` or 94%.