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If `E_1 and E_2` are two events associated with a random experiment such that `P (E_2)=0.35, P (E_1 or E_22)=0.85 and P(E_1 and E_2)=0.15,` then `P(E_

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If E1andE2 are two events associated with a random experiment such that P(E2)=0.35,P(E1orE22)=0.85andP(E1andE2)=0.15, then P(E1) is (A) .25 (B) .35 (C) .65 (D) .75 Select the correct answer from above options

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Let P ( E 1 ) = x . Then, P ( E 1 or E 2 ) = P ( E 1 ) + P ( E 2 ) − P ( E 1 and E 2 ) ⇒ 0.85 = x + 0.35 − 0.15 ⇒ x = ( 0.85 − 0.35 + 0.15 ) = 0.65 Hence, P ( E 1 ) = 0.65 .

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