If E and F are events such that `P(E) = 1/4, P(F) =1/2 and P(E and F) = 1/8,` find (i) `P(E or F)`, (ii) `P( - E and - F).`

Explanation

Given, `P(E)= 1/4​, P(F)= 1/2 `and `P(E and F) = 1/8`

(i) We know that `P(E uu F) = P(E) + P(F) - P(E nn F)`

`P (E uu F) = 1/4​+1/2​−1/8`
​=`(2+4−1​)/8=5/8`
​
(ii) `P(E∪F)=5/8`

We have `(E∪F)′=(E′∩F′)` [By De Morgan's law]

`P(E′∩F′)=P(E∪F)′`

Now `P(E∪F)′=1−P(E∪F)=1−5/8​=3/8`
​
`P(E′∩F′)=3/8`
​
...