Applied Mathematics

Probability Distribution

Medium

applied

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

0.3316

0.4216

0.2975

0.2150

✅ Correct Option: 3

With $n=100$ large and $p=0.018$ small, use the Poisson approximation with $\lambda=np=1.8$ .

$P(X=1)=\lambda e^{-\lambda}=1.8\times0.1653\approx0.2975$ .

2022: 25 May Shift 1

If the probability distribution of a random variable X is given as

$x_i$	0	1	2	3
$p_i$	$2k^2$	$k^2$	$3k^2$	$k$

Then the mean of X is

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: 29 May Shift 1

The mean of the number of tails in three tosses of a coin is :

2023: 7 June Shift 1

Match list I with list II. 4 defective pens are mixed with 10 normal pens. 3 pens are drawn one by one with replacement , then the probability distribution of the number of defective pens is :

List-I	List - II
A. P(X=0)	8/343
B. P(X=1)	60/343
C. P(X=2)	125/343
D. P(X=3)	150/343

Choose the correct option below :

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. The variance of a Poisson distribution with mean $\lambda$ is	I. $\sqrt{\lambda}$
B. The standard deviation of a Poisson distribution with mean $\lambda$ is	II. 4
C. In a Poisson distribution, if mean is 4, then the standard deviation is	III. $\lambda$
D. In a Poisson distribution, if mean is 4, then the variance is	IV. 2

Choose the correct answer from the options given below:

2026: 30 May Shift 2

In a printing press of a publication house, there is a small chance $\frac{1}{1000}$ for any typing error in 20 pages, then the number of pages containing no error in printing two volumes of an Encyclopedia containing total 10000 pages are:

[Given: $e^{-0.02}=0.9802$ ]

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=0.1653e^{-1.8}=0.1653e−1.8=0.1653)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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