For the three events `A ,B`, and `C` ,`P` (exactly one of the events `A or B` occurs)=`P` (exactly one of the two evens `B or C` )=`P` (exactly one of the events `C or A` occurs)=`p` and `P` (all the three events occur simultaneously)=`p^2` where `0`<`p`<`1//2`. Then the probability of at least one of the three events `A , B and C` occurring is

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`.