Applied Mathematics

Probability Distribution

Easy

applied

The mean and variance of a Binomial distribution are 4 and 4/3 respectively. The number of trials is

✅ Correct Option: 3

From $np=4$ and $npq=\frac{4}{3}$ we get $q=\frac{4/3}{4}=\frac{1}{3}$ , so $p=\frac{2}{3}$ . Then $n=\frac{4}{2/3}=6$ .

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 :

2023: 11 Aug Shift 1

2 voices dice are thrown together. For the first die $P(6) = \frac{1}{2}$ , other scores are equally likely. While for the second die $P(1) = \frac{2}{5}$ and other scores are equally likely than the Mean for the probability distribution of the number of one score will be

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Mean of a normal variate X is 12 and standard deviation is 4, then the Z-score of data point 20 is	(I) 1
(B) If X is Poisson variate such that P(X=1) = 2P(X=2), then the mean of X is	(II) 8
(C) In a binomial distribution, if mean is 5 and variance is 4, then the number of trials is	(III) 2
(D) In a binomial distribution, if n = 20 and q = 0.6, then its mean is	(IV) 25

Choose the correct answer from the options given below:

2026: 19 May Shift 2

A car hire firm has two cars, which is hire out day by day. The number of demands for cars on each day is distributed as a Poisson distribution with mean 1.5. Then which of the following is/are TRUE? (use $e^{-1.5} = 0.2231$ )

A. The probability of days when no car is required is 0.2231

B. The probability of days when some demand is refused is 0.1913

C. The probability of days when no car is required is 0.1913

D. The probability of days when some demand is refused is 0.2231

Choose the correct answer from the options given below:

2026: 29 May Shift 2

The probability distribution of a discrete random variable is given below :

X	1	2	3	4	5
P(X)	1/5	m	2/5	2m	3m

Which of the following are correct?

A. $P(2)=\frac{1}{15}$

B. $P(4)=\frac{2}{15}$

C. $P(X<2)=\frac{1}{5}$

D. $P(X\geq4)=\frac{1}{5}$

Choose the correct answer from the options given below:

2026: 18 May Shift 2

A pair of dice is thrown 5 times. If getting a total of 7 is considered a success, then

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Probability of no success	I. $26\left(\dfrac{1}{6}\right)^5$
B. Probability of 5 successes	II. $2\left(\dfrac{5}{6}\right)^5$
C. Probability of at least 4 successes	III. $\left(\dfrac{1}{6}\right)^5$
D. Probability of at most one success	IV. $\left(\dfrac{5}{6}\right)^5$

Choose the correct answer from the options given below:

The mean and variance of a Binomial distribution are 4 and 4/3 respectively. The number of trials is

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