1.

For three events A,B and CP (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 ir A occurs) = P and P(all the three events occur simultaneously) =P^(2), where 0ltplt(1)/(2) Then the probability of at least one of the three events A,B and C occuring is :

Answer»

`(3p+2p^(2))/(2)`
`(p+3p^(2))/(4)`
`(p+3p^(2))/(2)`
`(3p+3p^(2))/(4)`

Solution :P(exactly ONE of A or B occurs) `= P(A)+P(B)-2P(A nn B)`
SIMILARLY for B or C , C or A
Adding all THREE, we get,
`P(A)+P(B)+P(C )-P(A nn B)-P(B nn C)-P(C nn A)=(3p)/(2)`
`P(A uu B uu C)=(3p)/(2)+p^(2)`


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