If `A` and `B` are independent events such that `P(A)=p ,\ P(B)=2p` and `P` (Exactly one of `A` and `B` occurs )`=5/9` , find the value of `p`

Explanation

Given, `A` and `B` are independent events


`P(AnnB)=P(A) times P(B)=2p^2`


`P(A)=p, P(B)=2p`


`P`(Exactly one of `A` and `B`)`=5/9`


`[P(A)-P(AnnB)]+[P(B)-P(AnnB)]=5/9`


`[p-2p^2]+[2p-2p^2]=5/9`


`3p-4p^2=5/9`


`36p^2-27p+5=0`


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