A and B appear for an interview for two posts the probability of A's selection is 1/3 and that of B's selection is 2/5. Find the probability that only one of them will be selected ?  

CONCEPT:

• If P(A) = x then P(A̅) = 1 - x 
• If A and B are two independent events then P(A ∩ B) = P(A) × P(B)

CALCULATION:

Given: A and B appear for an interview for two posts such that the probability of A's selection is and that of B's selection is .

Let E = event that A is selected

Let F = event that B is selected

⇒ P(E) = and P(F) =

As we know that, if P(A) = x then P(A̅) = 1 - x 

⇒ P(E̅) = 1 - () = and P(F̅) = 1 - () =

∴ P(event that one of them is selected) = P(E ∩ F̅) + P(E̅ ∩ F)

First let's find out P(E ∩ F̅) and P(E̅ ∩ F)

As we know that, if A and B are two independent events then P(A ∩ B) = P(A) × P(B)

⇒ P(E ∩ F̅) = P(E) × P(F̅) = () × () =

⇒ P(E̅ ∩ F) = P(E̅) × P(F) = () × () = 

⇒ P(event that one of them is selected) = () + () = 

Hence, the correct option is 2.