Find the probability.

Question

In a university, the probability that a student takes calculus or is on scholarship is 0.85. The probability that a student is on scholarship is 0.61 and the probability that a student is taking calculus is 0.31. If a student is randomly chosen, find the probability that the student is taking calculus and is on scholarship.

Answer 1

P(CvS) = P(C) + P(S) - P(C^S)

P(C^S) = P(C) + P(S) - P(CvS) = .31+.61-.85 = .92-.85 = .07

P(C^S) = 0.07 C^S is the intersection. CvS is the union C is all students taking calculus S= all students on a scholarship.

There's a 7% chance a student is on a scholarship and taking calculus

it might be useful to draw a Venn diagram

15% take neither

draw a rectangle with two overlapping circles inside

put 15 for the area between the rectangle and the circles

the circles intersect with 7

students on just a scholarship and no calculus course is 61-7 = 54

students taking calculus and not on a scholarship are 31-7 = 24

24+54+7 + 15 = 100