Question

Suppose that all of the outcomes of a random variable are left curly bracket a comma space b comma space c comma space d right curly bracket, and that each outcome as an equal bevelled 1 fourth probability of occurring. Define the events A equals left curly bracket a comma b comma c right curly bracket, B equals left curly bracket c comma d right curly bracket, C equals left curly bracket d right curly bracket, and D={b,c}. True or false: The events B and D are independent.

True

False

Answer 1

P(B) = 2/4 = 1/2

P(D) = 2/4 = 1/2

There is one element common in B and D i.e. b. So,

P(B and D) = 1/4

P(B)P(D) = (1/2)*(1/2) = 1/4

Since P(B and D) = P(B)P(D)

B and D are independent.

The statement is True.