Question

The chance of solving a problem by A and B is and 1/3 and 2/5 respectively. What is the probability the problem will be solved?

a)2/15
b)1
c)9/15
d)11/15
Books shows "c" as the answer.. I am confused.. ​

Answer 1

We want to compute the probability P(A or B) because we could either solve it following path A, path B, or doing both paths.

P(A) = 1/3

P(B) = 2/5

P(A and B) = P(A)*P(B) assuming A,B are independent

P(A and B) = (1/3)*(2/5)

P(A and B) = 2/15

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

P(A or B) = 1/3 + 2/5 - 2/15

P(A or B) = 5/15 + 6/15 - 2/15

P(A or B) = (5 + 6 - 2)/15

P(A or B) = 9/15

We could reduce this to 3/5, but it appears your teacher has chosen not to.