Students are given three chances to pass a basic skills exam for permission to enrol in Calculus. Sixty percent of the students pass on the first try, of those that fail on the first try, fifty four percent pass on the second try, and of those remaining, forty eight percent pass on the third try.

a.What is the probability that a student passes on the second try?

b.What is the probability that a student passes on the third try?

c.What is the percentage of the student pass?

Can someone help me with this? I don't know how to solve it. Thank you!

To solve this problem, we can break it down into smaller steps and use the given information to find the probabilities.

a. To find the probability that a student passes on the second try, we need to find the probability of failing on the first try and then passing on the second try. Given that 60% of students pass on the first try, the probability of failing on the first try is 1 - 0.6 = 0.4. From the information given, 54% of those who fail on the first try pass on the second try. So, the probability of passing on the second try can be calculated as (0.4 * 0.54).

b. To find the probability that a student passes on the third try, we need to find the probability of failing on both the first and second tries and then passing on the third try. Given that 60% of students pass on the first try and 54% of those who fail on the first try pass on the second try, the probability of failing on both the first and second tries can be calculated as (0.4 * (1 - 0.54)). From the information given, 48% of those who fail on both the first and second tries pass on the third try. So, the probability of passing on the third try can be calculated as (0.4 * (1 - 0.54) * 0.48).

c. To find the percentage of students who pass, we need to consider all three scenarios: passing on the first try, passing on the second try, and passing on the third try. Given that 60% of students pass on the first try, the probability of passing on the second try can be calculated as (0.4 * 0.54) as in part a. Similarly, the probability of passing on the third try can be calculated as (0.4 * (1 - 0.54) * 0.48) as in part b. The overall probability of passing can be calculated by adding up the probabilities of passing from all three scenarios and then multiplying by 100 to convert it into a percentage. So, the percentage of students who pass can be calculated as (60 + (0.4 * 0.54) + (0.4 * (1 - 0.54) * 0.48)) * 100.

By using these steps, you can calculate the probabilities and the percentage of students who pass in this scenario.