The odds in favour of A solving a problem is 5:7 and Odds against B solvingthe same problem is 9:6. What is the probability that if both of them try, theproblem will be solved?(a) 117/180(b) 181/200(c) 147/180(d) 119/180

First, let's understand the odds and convert them into probabilities.

1. For A, the odds in favor of solving the problem are 5:7. This means that for every 5 times A solves the problem, there are 7 times A doesn't. So, the probability of A solving the problem is 5/(5+7) = 5/12.

2. For B, the odds against solving the problem are 9:6. This means that for every 9 times B doesn't solve the problem, there are 6 times B does. So, the probability of B solving the problem is 6/(9+6) = 6/15.

Now, we want to find the probability that the problem will be solved if both of them try. This means that we want to find the probability that either A solves the problem, or B solves the problem, or both.

The probability that at least one of two events will happen is given by the sum of the probabilities of the two events, minus the probability of both events happening at the same time.

So, the probability that the problem will be solved is:

P(A or B) = P(A) + P(B) - P(A and B)

We know P(A) and P(B), but we don't know P(A and B), the probability that both A and B solve the problem. However, we can assume that A and B are independent (the problem-solving of one doesn't affect the other), so P(A and B) = P(A) * P(B).

So, P(A or B) = P(A) + P(B) - P(A) * P(B) = 5/12 + 6/15 - (5/12 * 6/15) = 147/180.

So, the answer is (c) 147/180.