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If A and B are two independent events, t...

If A and B are two independent events, the probability that both A and B occur is 1/8 are the probability that neither of them occours is 3/8. Find the probaility of the occurrence of A.

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Verified by Experts

We have,
`P(AnnB)=1/8and P(barAnnbarB)=3/8`
`thereforeP(A)P(B)=1/8and P(barA)P(barB)=3/8`
`" "[therefore"A and B are independent"]`
Now, `P(barAnnbarB)=3/8`
`implies1-P(AnnB)=3/8`
`or 1-(P(A)+P(B)-P(AnnB))=3/8`
`or1-(P(A)+P(B))+1/8=3/8`
`orP(A)+P(B)=3/4`
The equation whose roots are P(A) and P(B) is `x^(2)-x{P(A)+P(B)}+P(A)P(B)=0`
`or x^(2)-3/4x+1/8=0`
`or8x^(2)-6x+1=0`
`or x=1/2,1/4`
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