The odds against an event are 7 : 3 and the odds in favour of another independent event are 5 : 2. The probability that at least one of the two events will occur is

Let, A = probability of first event taking place, P(A) = 3/(7 + 3) = 3/10. B = probability of second event taking place, P(B) = 5/(5 + 2) = 5/7. The event will occur if  either only A takes place and B does not take place or B takes place and A does not take place, or both the events take place. Therefore, the required probability will be = [P(A) x {1 - P(B)}] + [P(B) x {1 - P(A)}] + [P(A) x P(B)] = [3/10 x (1 - 5/7)] + [5/7 x (1 - 3/10)] + [3/10 x 5/7] = 4/5.