Question

Which of the following pairs of events are independent?

	Rolling a die and tossing a coin
	Rolling a sum of 12 on two dice and rolling a 6 on one of two dice
	Scoring in a soccer game and winning a soccer game
	All of the above are independent events
	None of the above are independent events

Answer 1

Independent events are independent if incidence of ome event does not affect the probability of other events.

Event A and B are independent if and only if

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

Let A rolling a summ of 12 on one dice

And B rolling a 6 on one of two dice

P(A and B) =1/36

P(A)=6/36

P(B) =6/36

P(A)P(B)=(6/36)(6/36)=1/36 =P(A B)

Hence rolling a sum of 12 and rolling 6 on one of two dice is independent.