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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 2 · Set 3 · Q31
(a) Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected,…
(a)
Two numbers are selected from first six even natural numbers at random without replacement. If $\displaystyle X$ denotes the greater of two numbers selected, find the probability distribution of X .
OR
(b)
A fair coin and an unbiased die are tossed. Let A be the event, "Head appears on the coin" and B be the event, " $\displaystyle 3$ comes on the die". Find whether $\displaystyle A$ and $\displaystyle B$ are independent events or not.
Marking-scheme solution
(a)
X: Greater of the two slected from first six even natural numbers
| $\displaystyle X$ | $\displaystyle 4$ | $\displaystyle 6$ | $\displaystyle 8$ | $\displaystyle 10$ | $\displaystyle 12$ |
| $\displaystyle P(X)$ | $\displaystyle \frac{1}{15}$ | $\displaystyle \frac{2}{15}$ | $\displaystyle \frac{3}{15}$ | $\displaystyle \frac{4}{15}$ | $\displaystyle \frac{5}{15}$ |
| Or | |||||
(b)
$\displaystyle \mathrm{S}=$ Sample space $\displaystyle =\{\mathrm{H1}, \mathrm{H} 2, \mathrm{H} 3, \mathrm{H4}, \mathrm{H5}, \mathrm{H6}, \mathrm{T1}, \mathrm{T2}, \mathrm{T3}, \mathrm{T4}, \mathrm{T5}, \mathrm{T6}\}$
$$\therefore \quad P(A)=\frac{6}{12}=\frac{1}{2}, P(B)=\frac{2}{12}=\frac{1}{6}, P(A \cap B)=\frac{1}{12}
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.