PLZ HELPPP PROBABILITY

Question

data for the students enrolled in a local high school are shown in the Venn diagram below.

alg 2 - 210

sophomores - 320

both - 85

if a student from the Hight school is selected at random. what is the probability that the student is a sophomore given that the student is enrolled in alg 2?

A. 85/ 210

B. 85/296

C. 85/405

D. 85/1600

2) which situation best describes conditional probability?

a. finding the probability of an event occurring 2 or more times

b. finding the probability of an event occurring only once

c. finding the probability of 2 independent events occurring at the same time

d. finding the probability of an event occurring giving another event had already occurred

Answer 1

1) Probability that a student is a sophomore given that the student is enrolled in Algebra:

As the question states "given that the student is enrolled in Algebra 2" means we only look at the Algebra 2 group. So, the denominator is the total number of Algebra 2 students which is 210.

The students who are both sophomores and in Algebra 2 are 85.

So,

P(sophomore | Algebra 2) = 85/210

Choice A

2) "Conditional probability" means the probability of one event happening given that another event has already happened. The keyword here is "given." So, the answer would be choice D.

Answer 2

AJ S. is correct, but here is why.

P(S|A) = P(S and A)/P(A)

P(S)= 320/445

P(A)=210/445

P(A and S)=85/445

P(S|A) = 85/445 divided by 210/445