Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Medium2 minQB

MathematicsMediuminteger

If $n (X) = (K + 1)$ , then the probability of selecting 2 subsets $A$ and $B$ of the set ' $X$ ' such that $B =$ $A^{C}$ is equal to $\frac{1}{2 ^{m - 1}}$ where $m - k$ is equal to

Answer:

Solution:

$n (X) = k + 1$

No. of ways to construct $A = 2^{k + 1}$

No. of ways to construct $B = 2^{k + 1}$

∴ Total ways to construct A and $B = 2^{k + 1} \times 2^{k + 1}$

Favourable ways to construct $A = 2^{k + 1}$

Favourable ways to construct $B$ such that $B = A^{C}$ is $= 1$

∴ Favourable ways $= 2^{k + 1} \times 1$

Required Probability $= \frac{2 ^{k + 1}}{( 2 ^{k + 1} ) ^{2}} = \frac{1}{2 ^{k + 1}}$ $\Rightarrow m - 1 = k + 1$ $\Rightarrow m - k = 2$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: QB

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