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Previous Year Question (PYQs)



If $X$ is the number of heads obtained in four tosses of a balanced coin. Define $ Y=\dfrac{1}{1+X} $ Find $P\left(Y=\frac{1}{3}\right)$





Solution

$Y=\frac{1}{3} \Rightarrow 1+X=3 \Rightarrow X=2$ So we need: $P(X=2)$ For 4 tosses: $P(X=2)=\binom{4}{2}\left(\frac12\right)^4$ $=\frac{6}{16}=\frac{3}{8}$


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