Question

OUT OF TORONY TreeOf the 48 students in a class, 40 are taking the class because it is a major requirement, and the other8 aretaking it as an elective. If two students are selected at random from this class, what is the probability that thefirst student is taking the class as an elective and the second is taking it because it is a major requirement?What is the probability that the first student is taking the class because it is a major requirement and thesecond student is taking the class as an elective?

Answer 1

First Question:

We have to multiply the probability of the two events:

First event: Selecting a student who is taking the class as an elective (8/48)

Second event: Selecting a student who is taking the class because it is a major requirement, after the first event happens. ( 40 / 47 ( We have to subtract one student from the total))

Multiplying both probabilities, we have:

$\frac{8}{48}\cdot\frac{40}{47}=\frac{320}{2256}=\frac{20}{141}\text{ (Simplifying)}$

The answer of the first question is: 20/141.

Second Question:

We have to multiply the probability of the two events:

First event: Selecting a student who is taking the class because it is a major requirement (40/48)

Second event: Selecting a student who is taking the class as an elective , after the first event happens. ( 8 / 47 ( We have to subtract one student from the total))

Multiplying both probabilities, we have:

$\frac{40}{48}\cdot\frac{8}{47}=\frac{320}{2256}=\frac{20}{141}\text{ (Simplifying)}$

The answer of the second question is: 20/141.