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 prime)=(1+λ)2 in terms of an unknown λ. Then P(E) is equal to

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 prime)=(1+λ)2 in terms of an unknown λ. Then P(E) is equal to (A) 1 (B) 3 / 4 (C) 1 / 4 (D) None of these

Tardigrade Admin · Accepted Answer

P(E)+P(E prime)=1=1+λ+λ2+(1+λ)2 or 2 λ2+3 λ+1=0 or (2 λ+1)(λ+1)=0 or λ=-1,-(1/2) Then, P(E)=1+(-1)+(-1)2=1 (not possible ) =1+(-(1/2))+(-(1/2))2=(1/2)+(1/4)=(3/4)

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

1

$3/4$

$1/4$

None of these

$P (E) + P (E^{'}) = 1 = 1 + λ + λ^{2} + (1 + λ)^{2}$
or $2 λ^{2} + 3 λ + 1 = 0$
or $(2 λ + 1) (λ + 1) = 0$
or $λ = - 1, - \frac{1}{2}$
Then, $P (E) = 1 + (- 1) + (- 1)^{2} = 1$ (not possible $)$
$= 1 + (- \frac{1}{2}) + (- \frac{1}{2})^{2} = \frac{1}{2} + \frac{1}{4} = \frac{3}{4}$

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 P(E′)=(1+λ)2 in terms of an unknown λ. Then P(E) is equal to

1

3/4

1/4

None of these

P(E)+P(E′)=1=1+λ+λ2+(1+λ)2 or 2λ2+3λ+1=0 or (2λ+1)(λ+1)=0 or λ=−1,−21​ Then, P(E)=1+(−1)+(−1)2=1 (not possible ) =1+(−21​)+(−21​)2=21​+41​=43​

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

$3/4$

$1/4$

$P (E) + P (E^{'}) = 1 = 1 + λ + λ^{2} + (1 + λ)^{2}$
or $2 λ^{2} + 3 λ + 1 = 0$
or $(2 λ + 1) (λ + 1) = 0$
or $λ = - 1, - \frac{1}{2}$
Then, $P (E) = 1 + (- 1) + (- 1)^{2} = 1$ (not possible $)$
$= 1 + (- \frac{1}{2}) + (- \frac{1}{2})^{2} = \frac{1}{2} + \frac{1}{4} = \frac{3}{4}$