GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 28

Answer 1

Here it is given that P(X = 0) = P(Y = 0) = P(X =1) = P(Y=1) = 0.5.

To find : P(X+Y <= 1) so it means  X+Y = 0 or X+Y =1 is only possible

P(X+Y =0) = P(X=0) and P(Y= 0) = 0.5 * 0.5 = 0.25.

P(X+Y =1) = P(X=1) and P(Y= 0)  OR P(X=0) and P(Y= 1)  = 0.5 * 0.5  + 0.5 * 0.5= 0.25 + 0.25 =0.5

so final answer we will get, 0.5 + 0.25 = 0.75

Comments

It should be  P(X = 0) = P(Y = 0) = P(X =1) = P(Y=1) = 0.5