Question

There are 100 students, when the instructor asks whether people have understood a particular proof, 25 students raise their hand. When he asks how many haven’t understood the proof, 35 raise their hands. The instructor notices that 10 students raise their hands in both cases. If he were to pick a student uniformly at random from the class, what is the probability that the student has not raised his hand in either case?

Answer 1

Here we are given n=100 and

n(understand)=25

n(not understand)=35

n(both)=10

N(not raises hand)=100-(25+35-10)=50

P(not raises hand)=50/100=0.5