Question

Mason rolls a 10 -sided number cube that represent the numbers1 through 10. He then rolls the number cube again. What is the probability that he rolls a number greater than 7 on his first roll and a multiple of 5 on his second roll?

A. 2/25
B. 3/5
C. 3/50
D. 3/100
E. 1/2

Answer 1

The probability that Mason rolls a number greater than 7 on his first roll and a multiple of 5 on his second roll with a 10-sided die is 3/50.

Step-by-step explanation:

The question asks what the probability is that Mason rolls a number greater than 7 on his first roll of a 10-sided die and a multiple of 5 on his second roll. There are three numbers greater than 7 on a 10-sided die (8, 9, 10), so the probability of rolling one of these on the first roll is 3/10.

To find the probability that Mason rolls a number greater than 7 on his first roll and a multiple of 5 on his second roll, we need to determine the number of favorable outcomes and the total number of possible outcomes. Since the number cube represents numbers 1 through 10, there are 4 outcomes greater than 7 (8, 9, 10), and 2 outcomes that are multiples of 5 (5, 10).

So, the number of favorable outcomes is 4 * 2 = 8. The total number of possible outcomes is 10 * 10 = 100 (since there are 10 options on each roll). Therefore, the probability is 8/100, which simplifies to 2/25.

The multiples of 5 on a 10-sided die are 5 and 10, so the probability of rolling a multiple of 5 is 2/10 or 1/5. To find the total probability of both events happening, we multiply the probabilities of each individual event occurring: (3/10) x (1/5) = 3/50. Therefore, the correct answer is C. 3/50.