. A biology class has 32 students. It is known that there are 18 females in the class and 15 science majors. Of the science majors 40% are female.

Question

Let F=Student is a female and S=Student is a science major.

Calculate the following probabilities:

(a) 𝑃(𝐹 𝑎𝑛𝑑 𝑆)

(b) 𝑃(𝐹 𝑜𝑟 𝑆)

(c) 𝑃(𝐹 ′𝑎𝑛𝑑 𝑆 ′ )

Answer 1

There are 15 science majors of which 40% are female, so there are 15 * 0.4 = 6 students who are female and science majors, meaning the probability is 6/32 that a student is female and a science major (part a).

Probability female (18/32) + probability science major (15/32) - probability female and science major (6/32) = 27/32 probability female or science major (part b)

If there is a 27/32 probability female or science major, then there is a 5/32 probability that it is neither (part c).