Question

mason rolls a 10-sided number cube that represents the numbers 1 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?

Answer 1

To calculate the probability that Mason rolls a number greater than 7 on his first roll and a multiple of 5 on his second roll, we multiply the individual probabilities of each event to find a combined probability of 3/50 or 6%.

Step-by-step explanation:

The subject of this question is Mathematics, and it pertains to the concept of probability with a specific focus on calculating the probability of multiple independent events occurring in sequence. 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 must consider the sample space and favorable outcomes for each event individually and then use the multiplication rule of probability.

For the first roll, the numbers greater than 7 are 8, 9, and 10. Therefore, the probability of rolling a number greater than 7 is 3 out of 10 (since there are 10 possible outcomes). For the second roll, the multiples of 5 in the range 1 to 10 are 5 and 10. This means the probability of rolling a multiple of 5 is 2 out of 10.

To find the combined probability of both events occurring, we multiply the probabilities of each individual event. Therefore, the probability that Mason rolls a number greater than 7 on his first roll and a multiple of 5 on his second roll is (3/10) * (2/10) = 6/100, which simplifies to 3/50 or 6%.