Question

You survey 80 people and ask them if they like plain m&ms or peanut m&ms. They can like either, both, or neither. You find 42 people like plain and 35 like peanut. You note that 28 like both. If you select one of these people at random, what is the probability that they like peanut and plain.

Answer 1

The number of people surveyed is 80

Out of these, 42 like plain while 35 like peanut and 28 like both.

Let A be the event the people like plain

Let B be the event the people like peanut

So, A⋂B denote the event that people like both plain and peanut

AUB denote the event that people like either plain or peanut

So P(A) = 42/80 and P(B) = 35/80

Also P(A⋂B) = 28/80

Now P(AUB) = P(A) + P(B) - P(A⋂B) = (42+35-28)/80

So, P(AUB) = 49/80

The probability that people like either plain or peanut is 49/80

The probability that people like both plain and peanut is 28/80 = 7/20