Question

62% of all students at a college still need to take another math class. If 4 students are randomly selected, find the probability that

a. Exactly 2 of them need to take another math class.
b. At most 2 of them need to take another math class.
c. At least 2 of them need to take another math class.
d. Between 2 and 3 (including 2 and 3) of them need to take another math class.

Answer 1

The student's question regarding the probability of different numbers of students needing another math class can be solved using the binomial probability formula across the various scenarios mentioned.

Step-by-step explanation:

To answer the student's question regarding the probability of various scenarios where students need to take another math class, we would use the binomial probability formula P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, C(n, k) is the combination of n items taken k at a time, and p is the probability of success on a single trial.

Calculating Each Probability

Exactly 2 need another math class: We calculate P(2) using the binomial formula with n=4 and p=0.62.

At most 2 need another math class: We add the probabilities P(0), P(1), and P(2).

At least 2 need another math class: We calculate 1 - (P(0) + P(1)).

Between 2 and 3 need another math class: We calculate P(2) + P(3).

Each scenario can be calculated using the above approach to obtain the respective probabilities.