Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityConditional probabilityMedium2 minPYQ_2021

MathematicsMediumsingle choice

A fair die is tossed until six is obtained on it. Let $X$ be the number of required tosses, then the conditional probability $P (X ⩾ 5 ∣ X > 2)$ is :

Options:

Answer:

Solution:

$P (\frac{x \geq 5}{x > 2}) = \frac{P (x \geq 5 \cap x > 2)}{P (x > 2)}$

$= \frac{{(\frac{5}{6})}^{4} \frac{1}{6} + {(\frac{5}{6})}^{5} \frac{1}{6} + . . . . . . . \infty}{{(\frac{5}{6})}^{2} \cdot \frac{1}{6} + {(\frac{5}{6})}^{3} \frac{1}{6} + \dots \dots \dots . \infty}$

$= \frac{\frac{{(\frac{5}{6})}^{4} \cdot \frac{1}{6}}{1 - \frac{5}{6}}}{\frac{{(\frac{5}{6})}^{2} \frac{1}{6}}{1 - \frac{5}{6}}} = {(\frac{5}{6})}^{2} = \frac{25}{36}$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Conditional probability

⏱ 2mℹ️ Source: PYQ_2021

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