Mathematics

Problem

In a college, every student may opt for cricket

(C)

and/or football

(F)

as extra-curricular activities. A survey reports the following probabilities:

P(C)=0.60

P(F)=0.30

P(F\mid C)=0.50

. a. (i) Find

P(C\cap F)

. (Show all steps.) b. (ii) Determine

P(C\mid F)

. (Write your answer correct to two decimal places.) c. (iii) On the basis of the above information, examine whether the events

C

and

F

are independent.