Probability of event

Question

The probabilities of Ahmad winning a badminton match and a chess game are 3/5 and 1/6. Find the probability that Ahmad only wins one of the match or game.

Answer 1

Pr(win match) = 3/5

Pr(win game) = 1/6

Pr(win both) = 3/5 x 1/6 =1/10

Pr(win neither) = 2/5 x 5/6 = 1/3

Pr(win match but not the game) = 3/5 x 5/6 = 1/2

Pr(win game but not the match) = 1/6 x 2/5 = 1/15

Pr(win one but not both) = 1/2 +1/15 = 17/30

1/3 + 1/10 + 17/30

= 10/30+3/30 +17/30

= 1

sum of probabilities of all 3 mutually exclusive outcomes: neither both or just one