A survey of 200 college students revealed the following likes: 128 students like…
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A survey of 200 college students revealed the following likes: 128 students like cricket (event C), 80 students like football (event F) and 48 students like both cricket and football. Answer the questions that follow.
(i) Express P(C), P(F) and P(C∩F) from the given data.
(ii) Calculate the probability that a randomly selected student likes cricket given that the student likes football, that is, find P(C∣F).
(iii) Calculate the probability that a student likes football given that the student likes cricket, that is, find P(F∣C).
(iv) Determine the probability that a student likes exactly one of the two sports.