A random variable $X$ denotes the number of accidents per year in a factory and the probability distribution of $X$ is given below : | $X = x$ | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | $p(x)$ | $4K$ | $15K$ | $25K$ | $5K$ | $K$ | (i) Find the constant $K$. (ii) Find the probability of the event that one or two accidents will occur in this factory during the year.

> > [!TLDR] > Sum of probabilities $= 50K = 1 \Rightarrow K = 0.02$; then $P(X = 1 \text{ or } 2) = 40K = 0.8$. > > GSEB Class-12 Statistics, Random Variable and Probability Mass Function: > > Given distribution: > > | $X = x$ | 0 | 1 | 2 | 3 | 4 | > |---|---|---|---|---|---| > | $p(x)$ | $4K$ | $15K$ | $25K$ | $5K$ | $K$ | > > **(i) Find $K$.** Since the total probability must equal $1$: > $$4K + 15K + 25K + 5K + K = 1$$ > $$50K = 1 \quad \Rightarrow \quad K = \frac{1}{50} = 0.02$$ > …

A random variable X denotes the number of accidents per year in a factory and the probability distribution of

Question 36 of 43

A random variable $X$ denotes the number of accidents per year in a factory and the probability distribution of $X$ is given below :

$X = x$	0	1	2	3	4
$p(x)$	$4K$	$15K$	$25K$	$5K$	$K$

Find the constant $K$ .
Find the probability of the event that one or two accidents will occur in this factory during the year.

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2025Subjective· 3mImportance★★★★★

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Sum of probabilities $= 50K = 1 \Rightarrow K = 0.02$ ; then $P(X = 1 \text{ or } 2) = 40K = 0.8$ .

GSEB Class-12 Statistics, Random Variable and Probability Mass Function:

Given distribution:

$X = x$	0	1	2	3	4
$p(x)$	$4K$	$15K$	$25K$	$5K$	$K$

(i) Find $K$ . Since the total probability must equal $1$ :

$4K + 15K + 25K + 5K + K = 1$

$50K = 1 \quad \Rightarrow \quad K = \frac{1}{50} = 0.02$

…

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set MARCH1 markMCQ
$Q. Which variable of the following will be an illustration of discrete variable?$
(a) Height of a student
(b) Weight of a student
(c) Blood pressure of a student
(d) Birth year of a student
›Reveal solutionSolution

Birth year takes countable whole-number values, so it is discrete.

A discrete variable assumes only isolated, countable values, whereas a continuous variable can take any value in an interval. Height, weight and blood pressure of a student are measured on a continuous scale, so they are continuous. The **birt …

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CBSE 2025Set MARCH1 markMCQ
$Q. Which variable of the following will be an illustration of continuous variable?$
(a) Number of accidents occurring at any place
(b) Number of rainy days during a year
(c) Maximum temperature during a day
(d) Number of children in a family
›Reveal solutionSolution
The maximum temperature during a day is a continuous variable, because it can take any value in an interval — option (c).

GSEB Class-12 Statistics, Random Variable chapter:

A discrete variable takes isolated (usually whole-number) values obtained by counting.

A continuous variable can take any value within a range and is obtained by measurement.

Checking the options:

Number of accidents — a count → discrete.

Number of rainy days — a count → discrete. …
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CBSE 2023Set MARCH1 mark
$Q. Define discrete random variable.$
›Reveal solutionSolution

A discrete random variable takes only countable (finite or countably infinite), isolated values.

A random variable is a real-valued function defined on the sample space of a random experiment. It is called a discrete random variable when the set of values it can assume is countable — either finite or countably infinite — and the values are distinct and separated (e.g. the number of heads in tosses of a coin, the number of defective items in a lot). Between two …

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CBSE 2022Set MARCH1 markMCQ
$Q. Which variable of the following will be an illustration of discrete variable?$
(a) Height of a student
(b) Weight of a student
(c) Blood pressure of a student
(d) Birth year of a student
›Reveal solutionSolution

Birth year takes only isolated whole-number values, so it is a discrete variable; height, weight and blood pressure are continuous.

Reasoning. A discrete variable can assume only specific separated values (usually counts), while a continuous variable can take any value in an interval. Height, weight and blood pressure can take any value on a …

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