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?

The probability of all events occurring is found by multiplying the probabilities of the individual events. I will do one of the problems for you.

b. (1-.6)(.4)(.46)(.48) = ?

P(fail 1st) = 1-.6

P(fail 2nd) = (.4)(.46)

This should give you and idea of the process to solve the other two problems.

To find the probabilities and percentages in this scenario, we can use conditional probability calculations. We'll break down the problem step-by-step using the given information.

a. Probability of passing on the second try:
From the given information, we are told that sixty percent (0.60) of the students pass on their first try. Therefore, the probability of failing on the first try is 1 - 0.60 = 0.40.

Out of the students who failed on the first try, fifty-four percent (0.54) pass on the second try. To find the probability of passing on the second try, we multiply the probability of failing on the first try by the probability of passing on the second try given the failure on the first try:
0.40 * 0.54 = 0.216

Therefore, the probability that a student passes on the second try is 0.216 or 21.6%.

b. Probability of passing on the third try:
From the previous calculations, we know that 40% (0.40) of the students failed on the first try. Out of these students who failed on both the first and second tries, 48% (0.48) pass on the third try.

To find the probability of passing on the third try, we multiply the probability of failing on the first try (0.40) by the probability of failing on the second try (0.46) and then multiply it by the probability of passing on the third try given the first two failures:
0.40 * 0.46 * 0.48 = 0.08832

Therefore, the probability that a student passes on the third try is 0.08832 or 8.832%.

c. Percentage of students who pass:
The percentage of students who pass can be found by adding up the probabilities of passing on the first, second, and third tries.

From the given information, we know that 60% (0.60) of the students pass on their first try, 21.6% (0.216) pass on their second try, and 8.832% (0.08832) pass on their third try.

Adding these probabilities together, we get:
0.60 + 0.216 + 0.08832 = 0.90432

Therefore, the percentage of students who pass is 90.432% or approximately 90.43%.