jmc

1. Identify the total number of ways to select two different numbers from the set: The set has 6 elements. The number of ways to choose 2 different numbers from 6 is given by the combination formula: $\left(\genfrac{}{}{0ex}{}{6}{2}\right)=\frac{6\times 5}{2\times 1}=15$. 2. Identify the favorable outcomes: For the product to be zero, one of the chosen numbers must be zero. The set contains one zero (0). To have a product of zero, we need to choose 0 and any other number from the remaining five numbers $-2,-1,3,4,5$. The number of ways to choose 0 and one other number from the remaining five is 5. 3. Calculate the probability: The probability is the number of favorable outcomes divided by the total number of outcomes: $\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{5}{15}=\frac{1}{3}$. Thus, the probability that the product is $0$ is $\boxed{\frac{1}{3}}.$