Each member of a class of 30 boys supports one and only one of the three football teams; 13 boys support city, 10 support Rovers, and 7 support United.
(i) If a boy is to be chosen at random, what is the probability that he will support City?
(ii) If 2 boys are to be chosen at random, what is the probability that they will both support City?
Find the probability that
(iii) two boys chosen at random will support the same team.
(iv) two boys chosen will support different teams.
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Answer:
(i) 13/30 (13 boys out of 30 boys)
(ii) P(both boys support City)
= P(1st boy support City) * P(2nd boy support City)
= 13/30 * 12/29
= 26/145
(iii) P(both boys support the same team)
= P(both boys support City) + P(both boys support Rovers) + P(both boys support United)
= 26/145 + 10/30 * 9/29 + 7/30 * 6/29
= 26/145 + 3/29 + 7/145
= 48/145
(iv) P(two boys chosen will support different teams)
= 1 - P(both boys support the same team)
= 1 - 48/145
= 97/145
