Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityTotal probability/Bay's TheoremMedium2 minPYQ_2018

MathematicsMediumsingle choice

A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $B$ is :

Options:

Answer:

Solution:

Probability that box $A$ is selected $P (A) = \frac{1}{2}$

Probability that box $B$ is selected $P (B) = \frac{1}{2}$

Let $E$ be the event that one ball is white while the other is red.

$∴ P (E) = P (A) \cdot P (E / A) + P (B) \cdot P (E / B)$

$= \frac{1}{2} [\frac{2 \cdot 3}{^{7} C_{2}} + \frac{4 \cdot 2}{^{9} C_{2}}] = \frac{1}{2} [\frac{6}{21} + \frac{8}{36}] = \frac{1}{2} [\frac{2}{7} + \frac{2}{9}] = \frac{16}{63}$

Thus, $P (B / E) = \frac{P (B) P (E / B)}{P (E)} = \frac{\frac{1}{9}}{\frac{16}{63}} = \frac{7}{16}$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Total probability/Bay's Theorem

⏱ 2mℹ️ Source: PYQ_2018

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