Question

Rolling dice Suppose you roll two fair, six-sided dice—one red and one green. Are the events “sum is 8” and “green die shows a 4” independent? Justify

your answer.

Short answer

Yes, not independent.

Step-by-step solution

Step 1. Given Information

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

Step 2. Concept Used

Conditional probability: $P\left(A\right|B)=\frac{P(AandB)}{P\left(B\right)}$

Step 3. Calculation

$P(sumis8/greendieshowsat4)=\frac{favourableoutcome}{possibleoutcomes}s=\frac{1}{6}$

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

P (sum is $7$) = $\frac{favourableoutcomes}{possibleoutcomes}=\frac{5}{36}$

Since$(2,6),(3,5),(4,4)(5,3)$ are all potential combinations to make $8,(6,2)$ If the events "sum is $8$" and "green die shows at $4$" are independent, these probability should be similar.