Question

Jason will roll two fair number cubes each numbered 1 to 6, then he will multiply the resulting numbers. In how many different ways can the product be an odd number?

Answer 1

To find the number of different ways the product can be an odd number, we need to consider the factors that result in an odd number. There are 3 odd numbers that can be rolled on one die, so the number of different ways the product can be an odd number is 9.

Step-by-step explanation:

To find the number of different ways the product can be an odd number, we need to consider the factors that result in an odd number. An odd number is the product of two numbers if and only if both numbers are odd. Since the product of two odd numbers is always odd, we just need to find the number of odd numbers that can be rolled on the two dice.

Since one die has the numbers {1, 2, 3, 4, 5, 6}, there are 3 odd numbers (1, 3, 5) that can be rolled on one die. We need to multiply this by the number of ways the other die can result in an odd number. Since the dice are fair and independent, each die has the same probability of rolling an odd number.

Therefore, the number of different ways the product can be an odd number is 3 * 3 = 9.