In the horse race, the horse Exaclibur's chances of winning are 1/6, the horse Noorjehan's chances are 1/10 and those of the horse Bombay are 1/8. If the race starts with twelve horses and only one horse wins, then what are the chances that one of these three horses will win?

Solution (By Examveda Team)

Horse E chances to win = 1/6.
Horse E chances to loose = 1- 1/6 = 5/6.
Horse N chances to win = 1/10.
Horse N chances to loose = 1 - 1/10 = 9/10.
Horse B chances to win = 1/8.
Horse b chances to loose = 1 - 1/8 = 7/8.
There are three possible situations which will satisfy the given conditions:
a) Horse E win and horses N and B lose. Probability of this event happening = (1/6*9/10*7/8) = 63/480 = 0.131
b) Horse N win and horses B and E lose. Probability of this event happening = (1/10*5/6*7/8) = 35/480 = 0.0729
c) Horse B win and horses E and B lose. Probability of this event happening = (1/8*5/6*9/10) = 45/480 = 0.093
Hence, the required probability is = (63/480 + 35/480+ 45/480) = 0.297.