For the three events `A`, `B` and `C`, `P`(exactly one of the events A or B occurs) `= P`(exactly one of the events B or C occurs) `=P`(exactly one of the events C or A occurs)`= p` and `P`(all the three events occur simultaneously) `= p^2`, where `0ltplt1/2`. Then, find the probability of occurrence of at least one of the events `A`, `B` and `C`.

Explanation

P(exactly one of the events A or B)=`P{(AnnoverlineB)uu(overlineAnnB)}`

`p=P(A)+P(B)-P(AnnB)`

`p=P(A)+P(C)-P(AnnC)`

`p=P(B)+P(C)-P(BnnC)`

`p^2=P(AnnBnnC)`

`P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnB)-P(BnnC)-P(AnnC)+P(AnnBnnC)`

`=(3p)/2+p^2`

`=(3p+2p^2)/2`.