If A and B are two independent events such that P(B)=27, P(A∪B')=0.8, then P(A) is equal to...

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If A and B are two independent events such that P(B)=27, P(A∪B&#039;)=0.8, then P(A) is equal to...

phonelookup1l6x · Accepted Answer

P(A∪B&#039;)=P(A)+P(B&#039;)–P(A∩B&#039;)  …..(1)Also,                P(A∩B&#039;)=P(A)-P(A∩B)P(A∪B&#039;)=P(A)+P(B&#039;)–P(A)-P(A∩B)⇒P(A∪B&#039;)=P(A)+P(B&#039;)–P(A)+P(A∩B)⇒P(A∪B&#039;)=P(B&#039;)+P(A∩B)⇒P(A∪B&#039;)=1-P(B)+P(A).P(B) ….(2)     ∵P(B&#039;)=1-P(B),P(A∩B)=P(A).P(B)0.8=1-27+P(A).27⇒     0.8=57+27×P(A)⇒5+2P(A)=5.6⇒         2P(A)=0.6∴P(A)=0.3

If A and B are two independent events such that P(B)=27, P(A∪B')=0.8, then P(A) is...

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