The variance of the Binomial Distribution B(5, 1/4) is: Option 1: 4/5 Option 2: 7/8 Option 3: 15/16 Option 4: 4/7

Answer: 15/16. Solution: For B(n, p): variance = npq. Here n = 5, p = 1/4, q = 3/4. So variance = 5 * (1/4) * (3/4) = 15/16.

Applied Mathematics

Probability Distribution

Easy

applied

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

$\frac{4}{5}$

$\frac{7}{8}$

$\frac{15}{16}$

$\frac{4}{7}$

✅ Correct Option: 3

For $B(n, p)$ : variance $= npq$ . Here $n = 5$ , $p = 1/4$ , $q = 3/4$ . So variance $= 5 \cdot (1/4) \cdot (3/4) = 15/16$ .

2024: 16 May Shift 1

$X$	-2	-1	0	1	2
$P(X)$	$0.2$	$0.1$	$0.3$	$0.2$	$0.2$

The variance of $X$ will be :

2023: 11 Aug Shift 1

10 works hard drawn successively with replacement from a lot containing 10% defective bulb. The probability that there is at least one defective bulb is :

2026: 29 May Shift 1

A random variable X has the following probability distribution:

X	0	1	2	3	4
P(X)	0.1	0.15	0.30	0.30	0.15

Which of the following are correct?

(A) $P(X \le 1)=0.25$

(B) $P(X>3)=0.15$

(D) $P(X \le 2)=0.55$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) In a binomial distribution, if $n = 10$ , $q = 0.25$ , then its mean is	(I) 12
(B) If the mean of a binomial distribution is 6 and its variance is 3, then p is	(II) 7.5
(C) In a binomial distribution, the probability of getting a success is $\frac{1}{4}$ and the standard distribution is 3, then its mean is	(III) 16
(D) If the mean and variance of a binomial distribution are 4 and 3 respectively, then the number of trials is	(IV) $\frac{1}{2}$

Choose the correct answer from the options given below :

2026: 22 May Shift 2

The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 100 men, now aged 35 years, what is the approximate probability that one man will die within next five years?

(Given: $e^{-1.8}=0.1653$ )

2026: 15 May Shift 1

A coin is tossed until a head appears, or the tail appears 4 times in succession, then the probability distribution of the number of tosses is

The variance of the Binomial Distribution B(5,14)B\left(5, \frac{1}{4}\right)B(5,41​) is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is: