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Question

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

A
1
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B
3/4
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C
1/4
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D
none of these
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Solution

The correct option is B 3/4
Let E be an event which is neither certainty nor an impossibility.
Given, P(E)=1+λ+λ2
P(E)=(1+λ)2
P(E)+P(E)=0
1+λ+λ2+(1+λ)2=0
1+λ+λ2+1+2λ+λ2=0
2+3λ+2λ2=0
3λ=(2+2λ2)
3λ2=1+λ2
Neglect negative sigh, put λ=1
λ=34.
Hence, the answer is 34.

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