The probability distribution for the number of students being absent in a class on a Saturday is as follows : X 0 2 4 5 --- --- --- --- --- P(X) p 2p 3p p Where X is the number of students absent. (i) Calculate p. (ii) Calculate the mean of the number of absent students on Saturday.

MathsCBSE Class 12 · Board exam 2025, set 65/1/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2025: question 30(a)

Set in the CBSE Class 12 board exam of 2025, paper 65/1/1, section C, question 30(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(a) · 3 marks · Short answerCompetency-basedProbability

The probability distribution for the number of students being absent in a class on a Saturday is as follows :

X	0	2	4	5
P(X)	p	2p	3p	p

Where X is the number of students absent.

(i)
Calculate p.
1 mark
(ii)
Calculate the mean of the number of absent students on Saturday.
2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The probabilities in a distribution must add up to 1.

Hint 2

The mean is $\sum X \cdot P (X)$ . Express it in terms of $p$ first.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) Since $\sum P (X) = 1$ : $p + 2 p + 3 p + p = 1$ .
½ mark
(i) So $7 p = 1 \Rightarrow p = \frac{1}{7}$ .
½ mark
(ii) Mean $= \sum X P (X) = 0 (p) + 2 (2 p) + 4 (3 p) + 5 (p)$ .
1 mark
(ii) Mean $= 21 p = 21 \times \frac{1}{7} = 3$ .
1 mark

Answer: (i) $p = \frac{1}{7}$ ; (ii) Mean = 3

Where the marks are

Uses $\sum P (X) = 1$ (½ mark)
Gets $p = \frac{1}{7}$ (½ mark)
Writes the mean as $\sum X P (X)$ with the values substituted (1 mark)
Gets mean $= 3$ (1 mark)

Revise the chapter

Chapter: Probability (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 30(a)

Hints

Step-by-step solution

Revise the chapter

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