The probability that John solved a particular problem is 1/3 and the probability that James solved the same problem is 1/5, if they both attempt the problem, what is the probability that it will be solved by at least one of them?
Prob(John can't solve) = 2/3
prob(james can't solve = 4/5
prob = 1 - prob(both don't solve)
= .....
To find the probability that the problem will be solved by at least one of them, we can use the concept of complementary probability. The complementary event to "at least one of them solves the problem" is "neither John nor James solves the problem."
Let's first calculate the probability that neither John nor James solves the problem:
P(neither John nor James solves) = P(John doesn't solve) * P(James doesn't solve)
Since John has a probability of 1/3 of solving the problem, the probability that he doesn't solve it is 1 - 1/3 = 2/3.
Similarly, the probability that James doesn't solve the problem is 1 - 1/5 = 4/5.
P(neither John nor James solves) = (2/3) * (4/5) = 8/15
Now, we can find the probability that at least one of them solves the problem by subtracting the probability that neither of them solves from 1:
P(at least one of them solves) = 1 - P(neither John nor James solves)
= 1 - 8/15
= 7/15
Therefore, the probability that the problem will be solved by at least one of them is 7/15.