Help please math question?

Question

Suppose that a certain college contains 40 students. of these,22 are sophomores,23 are mathematics majors, and 11 are neither. A student is selected at random from the class

(a) What is the probability that the student is both a sophomore and mathematics major?

(b) Given that the student selected is a sophomore, what is the probably that she is also a mathematics major?

Write your response as a fraction

Answer 1

A good way to do this type of problem on paper would be to use a venn diagram. But, since I can't really show that, another way:

a) There are a total of 40 students. If 11 of these students are neither a math major or a sophomore, that means 29 of them are one or the other. Of these 29 "either or" students, 22 are sophomores, which leaves 7 leftover. These 7 have to be math majors which are not sophomores. However, you know that there are 23 math majors. Therefore, 23-7=16 of these math majors must also be sophomores. As such, the probability is 16/40 or 2/5.

b) You already know that the student selected is a sophomore. This part of the question assumes that. Therefore, you have to figure out how many of the sophomores are math majors. We already did that: 16. This time, you would do 16/22 (you do out of 22 instead of 40 since it is out of the sophomores, not the class), which reduces to 8/11.

Answer 2

ok... first write out your fractions your dealing with:

22/40 are sophomores

23/40= math majors

11/40 neither

so a) 22/40 * 23/40 is 506/1600 which can be reduced

and b) 23/40

im not sure if the answers are right... but there you go.

Answer 3

draw a venn daigram it clears things up

E=40

(S)sophomores=6

(M)math major=7

both math and sophomores=16

a) 16/40

2/5

b)16/22

8/11