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

1 Answer
Apr 7, 2018

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%.