The probability of a horse A winning a race is `(1)/(4)` and that of a horse B winning the same race is `(1)/(3)`. Considering that winning is matually exclusive, find the probability that
(i) Either of them win
(ii) None of them win

Explanation

(i) Let A be event horse A wins the race and B be the event horse B wins the race.
Then, `AcupB` = event " either of the horses A or B wins the race"
Thus, (i) `P(AcupB) = P(A) + P(B)`
`(1)/(4)+(1)/(3)=(7)/(12)`
(ii) Now, P(none of the horses win the race) = `P(A'cupB')`
`P(AcupB')`
= `1-P(AcupB)=1-(7)/(12)=(5)/(12)`