Fifty percent of students enrolled in calculus class have previously taken pre-calculus. Thirty percent of these students received an A for the calculus class, whereas twenty percent of the other students received an A for calculus. Find the probability that a student selected at random previously took pre-calculus and did not receive an A in the calculus class.

100 students

50 had pre calc - 15 got A, 35 not A

50 no pre cacl - 10 got A, 40 not A

sure looks like 35 of the hundred :)

Thanks Damon! :-)

You are welcome :)

There are 80 students enrolled statistics. Forty percent f the class received a grade of C. How many received a C?

To find the probability that a student selected at random previously took pre-calculus and did not receive an A in the calculus class, we need to use conditional probability.

Let's break down the given information:

1. Fifty percent of students enrolled in calculus class have previously taken pre-calculus. This means that the probability of a student previously taking pre-calculus is P(Pre-calculus) = 0.50.

2. Thirty percent of students who previously took pre-calculus received an A in the calculus class. This means that the probability of receiving an A given that the student previously took pre-calculus is P(A | Pre-calculus) = 0.30.

3. Twenty percent of students who did not previously take pre-calculus received an A in the calculus class. This means that the probability of receiving an A given that the student did not previously take pre-calculus is P(A | Not Pre-calculus) = 0.20.

We need to find the probability that a student selected at random previously took pre-calculus and did not receive an A in the calculus class, which is represented as P(Pre-calculus and Not A).

We can use the formula for conditional probability:

P(A and B) = P(A | B) * P(B)

In this case, A represents "Not A" (not receiving an A in calculus) and B represents "Pre-calculus".

Applying the formula, we get:

P(Pre-calculus and Not A) = P(Not A | Pre-calculus) * P(Pre-calculus)

P(Not A | Pre-calculus) is equal to 1 - P(A | Pre-calculus) because we want the probability of not receiving an A given that the student previously took pre-calculus.

So,

P(Pre-calculus and Not A) = (1 - P(A | Pre-calculus)) * P(Pre-calculus)

P(Pre-calculus and Not A) = (1 - 0.30) * 0.50

P(Pre-calculus and Not A) = 0.70 * 0.50

P(Pre-calculus and Not A) = 0.35

Therefore, the probability that a student selected at random previously took pre-calculus and did not receive an A in the calculus class is 0.35 or 35%.