Two horses are considered for a race. The probability of selection of the first horse is 1/4 and that of the second is 1/3. What is the probability that :(a) both of them will be selected. (b) only one of them will be selected. (c) none of them will be selected.

Let A be the event that the first horse is selected.Now, PA = 14  Pfirst horse is not selected =PA = 1 -  PA = 1 - 14 = 34Let B be the event that second horse is selected.Now, PB = 13 Psecond horse is not selected = PB = 1 -  PB = 1 - 13 = 231.Pboth selected =PAB =  PA . PB = 14 × 13 = 1122.Pexactly one is selected = PAB + PA¯B =  PA . PB  +  PA . PB = 14×23+34×13 = 5123Pnone of them is selected =PAB = PA . PB = 34×23 = 12

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