In a group of 120 people, 85 have black hair, 78 have brown eyes and 20 have neither black hair nor brown eyes. Find the probability of a random person being picked having black hair, given they have brown eyes

We are told that the person already has brown eyes, and this includes 78 people.We are asked to find the probability of them also having black hair.This means the person has to have brown eyes and black hair.The number of people with brown eyes and black hair is 85+78+20-120, as this calculates how much overlap there is, and the only overlap possible is between brown eyes and black hair. This equals 63.The number of people with brown eyes is 78, and the number of people with black hair and brown eyes is 63, so the probability of someone having black hair, knowing they have brown eyes is:(No. of people with black hair+brown eyes)/(Total no. of people with brown eyes) = 63/78 = 0.808 3.S.F.Answer is 0.808