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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 1 · Q31
(a) The probability that a student buys a colouring book is 0 · 7 and that she buys a box of colours is 0 · 2. The probability that she buys a…
The probability that a student buys a colouring book is $\displaystyle 0 \cdot 7$ and that she buys a box of colours is $\displaystyle 0 \cdot 2$. The probability that she buys a colouring book, given that she buys a box of colours, is $\displaystyle 0 \cdot 3$. Find the probability that the student:
(i)
Buys both the colouring book and the box of colours.
(ii)
Buys a box of colours given that she buys the colouring book.
A person has a fruit box that contains $\displaystyle 6$ apples and $\displaystyle 4$ oranges. He picks out a fruit three times, one after the other, after replacing the previous one in the box. Find :
(i)
The probability distribution of the number of oranges he draws.
(ii)
The expectation of the random variable (number of oranges).
Marking-scheme solution
(a)
Let A be the event of buying colouring book and $\displaystyle \mathrm{B}$ be the event of buying coloured box.
\[\mathrm{P}(\mathrm{A})=0.7, \quad \mathrm{P}(\mathrm{B})=0.2, \quad \mathrm{P}(\mathrm{A} / \mathrm{B})=0.3
\]
(i)
$\displaystyle \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})} \Rightarrow 0.3=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{0.2}$
\[\Rightarrow \mathrm{P}(\mathrm{A} \cap \mathrm{B})=0.06 \text { or } \frac{3}{50}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.