The probabilities of Arsenal, Liverpool, Chelsea or Manchester United winning the
Premier League Football Champions are 1/5, 1/6, 1/7 and 1/8 respectively.
Assuming only one team can win the championship, find the probability that
(i) either Arsenal or Liverpool wins the championship,
(ii) Liverpool or Chelsea or Manchester United wins the championship,
(iii) none of these teams wins the championship.
i) Prob(Ars or Liv) = 1/5 + 1/6 = 11/30 or appr .367
ii) same way as i)
iii) pro(one of the given teams wins) = 1/5+1/6+1/7+1/8 = 533/840
so prob(somebody else wins) = 1 - 533/840 = 307/840 or appr .365
(i)P(Arsenal wins) + P(Liverpool wins)
= 1/5 + 1/6 = 6/30 + 5/30 = 11/30
(ii) P(Liverpool wins) + P(Chelsea wins) +
P(Manchester United wins) = 1/6 + 1/7 + 1/8
= 28+24+21/168
= 73/168
(iii) P(Arsenal wins) + P(all 3 teams win)
= 1/5 + 73/168 } answer from (ii)
= 168+365/840 = 533/840
I-P(all 4 teams win) = 1 - 533/840 = 307/40