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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 4 · Set 2 · Q6
There are two bags. Bag I contains 1 red and 3 white balls, and Bag II contains 3 red and 5 white balls. A bag is selected at random and a ball is…
There are two bags. Bag I contains $\displaystyle 1$ red and $\displaystyle 3$ white balls, and Bag II contains $\displaystyle 3$ red and $\displaystyle 5$ white balls. A bag is selected at random and a ball is drawn from it. Find the probability that the ball so drawn is red in colour.
Marking-scheme solution
\(\displaystyle E_{1}\) : Bag $\displaystyle 1$ is selected
\(\displaystyle E_{2}\) : Bag $\displaystyle 2$ is selected
\(\displaystyle A\) : Ball drawn is red in colour
\[\begin{aligned}
P(A) & =P\left(E_{1}\right) P\left(A \mid E_{1}\right)+P\left(E_{2}\right) P\left(A \mid E_{2}\right) \\
& =\frac{1}{2} \times \frac{1}{4}+\frac{1}{2} \times \frac{3}{8} \\
& =\frac{5}{16}
\end{aligned}
\]
\[\begin{aligned}
P(A) & =P\left(E_{1}\right) P\left(A \mid E_{1}\right)+P\left(E_{2}\right) P\left(A \mid E_{2}\right) \\
& =\frac{1}{2} \times \frac{1}{4}+\frac{1}{2} \times \frac{3}{8} \\
& =\frac{5}{16}
\end{aligned}
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.