ethan rolls the number cube and then spins the arrow on the spinner. a list of all the possible outcomes is…

ethan rolls the number cube and then spins the arrow on the spinner. a list of all the possible outcomes is shown. {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)} what is the probability that the sum of the two numbers is odd, given that the product is 6? a. $\frac{1}{3}$ b. $\frac{1}{2}$ c. $\frac{2}{3}$ d. 1

ethan rolls the number cube and then spins the arrow on the spinner. a list of all the possible outcomes is shown. {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)} what is the probability that the sum of the two numbers is odd, given that the product is 6? a. $\frac{1}{3}$ b. $\frac{1}{2}$ c. $\frac{2}{3}$ d. 1

Answer

Answer:

C. $\frac{2}{3}$

Explanation:

Step1: Find pairs with product 6

The pairs with product 6 are $(2,3),(3,2),(6,1)$.

Step2: Calculate sum of pairs

For $(2,3)$: $2 + 3=5$ (odd). For $(3,2)$: $3+2 = 5$ (odd). For $(6,1)$: $6 + 1=7$ (odd).

Step3: Calculate probability

There are 3 pairs with product 6, and 2 of them have an odd - sum. So the probability is $\frac{2}{3}$.