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The probability of A solving a problem is 3/5 and the probability of B solving the problem is 1/3. If both of them work on the same problem then what is the probability that the problem will be solved?

The probability of A solving a problem is 3/5 and the probability of B solving the problem is 1/3. If both of them work on the same problem then what is the probability that the problem will be solved? Correct Answer 11/15

GIVEN:
A's solving probability = 3/5

B's solving probability = 1/3

CONCEPT:

Total probability of an event happening and not happening is 1.

For 'or' addition function and for 'and' multiplication function is applied.

FORMULA USED:
P = Favorable outcomes/Total outcomes

CALCULATION:

A's not solving P = 1- 3/5 = 2/5

B's not solving P = 1- 1/3 = 2/3
There are three cases, 

1st: A solves and B doesn't,

P (1) = 3/5 × 2/3 = 2/5

2nd: B solves and A doesn't

P (2) = 1/3 × 2/5 = 2/15

3rd: A and B both solve

P (3) = 3/5 × 1/3 = 1/5

∴ Required P = 2/5 + 2/15 + 1/5 = 11/15

∴ The probability is 11/15.

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