Suppose a sample space contains events E and F such that PrE

Suppose a sample space contains events E and F such that; Pr[E]=3/5 and Pr[F]=4/5 Find the smallest value of Pr[EF]

Solution

E and F are in the sample space

P(S) = prob for entire sample space = 1

Hence P(E)+P(F)-P(EF) =1

P(EF) = P(E)+P(F)-1

= 3/5 + 4/5 -1

= 2/5

P(EF) should be atleast 2/5