CBSE 2023 · Region 3 · Set 2 · Q37 · 4 marks

An octagonal prism is a three-dimensional polyhedron bounded by two octagonal bases and eight rectangular side faces. It has $\displaystyle 24$ edges and $\displaystyle 16$ vertices.

The prism is rolled along the rectangular faces and number on the bottom face (touching the ground) is noted. Let X denote the number obtained on the bottom face and the following table give the probability distribution of X.

$\displaystyle \mathrm{X}:$	$\displaystyle 1$	$\displaystyle 2$	$\displaystyle 3$	$\displaystyle 4$	$\displaystyle 5$	$\displaystyle 6$	$\displaystyle 7$	$\displaystyle 8$
$\displaystyle \mathrm{P}(\mathrm{X}):$	p	$\displaystyle 2$ p	$\displaystyle 2$ p	p	$\displaystyle 2$ p	$\displaystyle \mathrm{p}^{2}$	$\displaystyle 2 \mathrm{p}^{2}$	$\displaystyle 7 \mathrm{p}^{2}+\mathrm{p}$

Based on the above information, answer the following questions :

(i)

Find the value of p.

(ii)

Find $\displaystyle \mathrm{P}(\mathrm{X}>6)$.

(iii)

(a)OR(b)

Find $\displaystyle \mathrm{P}(\mathrm{X}=3 \mathrm{~m})$, where m is a natural number.

CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.