If it is given that the probability that `A` can solve the same problem is `(3)/(5). ` The probability that `B` can solve the same problem is `(2)/(3). `The probability that at least one of `A` and `B` can solve a problem is

Options

A. `(2)/(5)`
B. `(1)/(15)`
C. `(13)/(15)`
D. `(2)/(15)`

Answer

C

Explanation

Let `E_(1)` be the event the A can solve the problem and `E_(2)` be the event that B cab solve the problem . Then `E_(1) " and "E_(2)` are independent .
`:. P(E_(1) nnE_(2))=P(E_(1))xx P(E_(2)) =((3)/(5)xx (2)/(3)) =(2)/(5)`
` :. P(E_(1) uu E_(2)) =P(E_(1))+P(E_(2)) -P(E_(1) nnE_(2)) =((3)/(5)+(2)/(3) -(2)/(5))=(13)/(15)`