Question

Suppose that you have applied to two graduate schools and believe that you have a 0.6 probability of being accepted by school C, a 0.7 probability of being accepted by school D, and a 0.5 probability of being accepted by both.

A) Events (accepted by school C) and (accepted by school D) are independent. True or False

B) Events (accepted by school C) and (accepted by school D) are disjoint. True or False

Answer 1

Solution:

Given:

P( being accepted by school C) =0.6 ,

that is: P(C) =0.6

P( being accepted by school D) =0.7,

that is: P(D) =0.7

and

P( being accepted by both school C and D) =0.5 ,

that is: P(C and D ) =0.5

Part A) Events (accepted by school C) and (accepted by school D) are independent.

Two events A and B are independent if and only if :

P( A and B) = P(A) X P(B)

Thus we have to show:

P( C and D) =P(C) X P(D)

Lets find : P(C) X P(D)=..........?

P(C) X P(D)= 0.6 X 0.7

P(C) X P(D)= 0.42

Since P(C and D ) =0.5 and P(C) X P(D)= 0.42, that means both are not equal, thus events (accepted by school C) and (accepted by school D) are NOT independent.

Thus given statement is False.

Part B) Events (accepted by school C) and (accepted by school D) are disjoint.

Events A and B are disjoint , if

P( A and B) = 0

Since

P(C and D ) =0.5 which is not equal to 0.

Thus events (accepted by school C) and (accepted by school D) are NOT disjoint.

Thus statement given part B) is False.