One of the two events A and B must occur. If P(A)=12P(B) the odds in favour of B is

P(A)=12P(B)odds in favour of B is P(B):P(B¯)P(A)+P(B)=123P(B)+P(B)=15P(B)=3∴P(B)=35P(B¯)=25∴P(B):P(B¯)=3:2

One of the two events A and B must occur. If P(A)=12P(B) the odds in favour of B is

P(A)=12P(B)odds in favour of B is P(B):P(B¯)P(A)+P(B)=123P(B)+P(B)=15P(B)=3∴P(B)=35P(B¯)=25∴P(B):P(B¯)=3:2

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One of the two events $A$ and $B$ must occur. If $P (A) = \frac{1}{2} P (B)$ the odds in favour of $B$ is

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$2 : 1$

$1 : 2$

$2 : 3$

$3 : 2$

answer is D.

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Detailed Solution

$P (A) = \frac{1}{2} P (B)$

odds in favour of $B$ is $P (B ) : P (\bar{B})$

$\begin{array}{l} P (A) + P (B) = 1 \\ \frac{2}{3} P (B) + P (B) = 1 \\ 5 P (B) = 3 \\ ∴ P (B) = \frac{3}{5} \\ P (\bar{B}) = \frac{2}{5} \\ ∴ P (B) : P (\bar{B}) = 3 : 2 \end{array}$

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One of the two events $A$ and $B$ must occur. If $P (A) = \frac{1}{2} P (B)$ the odds in favour of $B$ is