Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x+y = 11} and B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.

Question

Philoid · Accepted Answer

We Have, A= {(x, y):x+y=11}

And B= {(x, y): x≠5}

∴ A = {(5,6), (6,5)}

B= {(1,1), (1,2), (1,3), (1,4), ((1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

n(A)=2, n(B)= 30, n(AՈB) = 1

∴

So, A and B are not independent.

Two dice are tossed. Find whether the following two events A and B are independent:A = {(x, y): x+y = 11} and B = {(x, y): x ≠ 5}where (x, y) denotes a typical sample point.

Two dice are tossed. Find whether the following two events A and B are independent:
A = {(x, y): x+y = 11} and B = {(x, y): x ≠ 5}

where (x, y) denotes a typical sample point.