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Q.

Let E be an event which is neither a certainty nor an impossibility. If probability is such that P(E)=1+λ+λ2 and PE'=(1+λ)2 in terms of an unknown λ. Then P(E) is equal to

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a

1

b

34

c

14

d

none of these

answer is B.

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Detailed Solution

P(E)+PE'=1∴ 1+λ+λ2+(1+λ)2=1⇒ 2λ2+3λ+1=0⇒ (2λ+1)(λ+1)=0⇒ λ=−1,−12For λ=−1,P(E)=1+(−1)+(−1)2=1 (not possible)For λ=−12,P(E)=1+−12+−122=12+14=34
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Let E be an event which is neither a certainty nor an impossibility. If probability is such that P(E)=1+λ+λ2 and PE'=(1+λ)2 in terms of an unknown λ. Then P(E) is equal to