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 
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.
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