A fair die is rolled. Consider events E = {1, 3, 5} ,  F = {2, 3}  and G= {2, 3, 4, 5} then find P((E∪F)IG)-

3/4

When a fair die is rolled, the sample space S will be S = {1, 2, 3, 4, 5, 6}

It is given that E = {1, 3, 5} ,  F = {2, 3}  and G= {2, 3, 4, 5}

So, P(E) = 3/6 = 1/2

P(F) = 2/6 = 1/3

P(G) = 4/6 = 2/3

We know that P((E∪F)IG) = P((E∪F)∩G)/ P(G)

E∪F = {1, 2 , 3 , 4}

(E∪F)∩G = {1, 2 , 3 , 4}∩{2, 3, 4, 5} = {2, 3, 5}

P{(E∪F)∩G} = 3/6= 1/2 

Hence  P((E∪F)IG) = (1/2)/(2/3) = 3/4