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Rolling dice Suppose you roll two fair, six-sided dice鈥攐ne red and one green. Are the events 鈥渟um is 7鈥 and 鈥済reen die shows a 4鈥 independent? Justify

your answer.

Short Answer

Expert verified

Yes, independent.

Step by step solution

01

Step 1. Given Information

Two fair rolls, one with a red face and the other with a green face.

02

Step 2. Concept Used

Definition condition probability:P(A|B)=P(AandB)P(B)

03

Step 3. Explanation 

P(sumis7greendieshowsat4)=favorableoutcomespossibleoutcomes=16

Since the red die must be a 3 in order for the total to be 7 (knowing that the green die shows at 4).

P(sumis7)=favorableoutcomespossibleoutcomes=636=16

Since the number 7 can be made in a variety of ways, (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

If the events "sum is 7" and "green die shows at 4" are independent, this probability should be similar. As a result, they are self-sufficient.

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