Applied Mathematics

Probability Distribution

Medium

applied

For 6 trials of an experiment, let X be a binomial variate which satisfies the relation $9P(X=4)=P(X=2)$ , then the probability of success is

$\dfrac{1}{2}$

$\dfrac{1}{3}$

$\dfrac{1}{4}$

$\dfrac{2}{3}$

✅ Correct Option: 3

With $n=6$ , $9\binom{6}{4}p^4q^2 = \binom{6}{2}p^2q^4$ .

Since $\binom{6}{4} = \binom{6}{2}$ , this reduces to $9p^2 = q^2$ , so $3p = q = 1-p$ .

Hence $4p = 1$ and $p = \dfrac{1}{4}$ .

2026: 29 May Shift 1

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

2023: 22 May Shift 3

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$ , then $P(X \leq 9)$ is :

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: 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: 18 May Shift 1

Which of the following statements are correct?

(A) The mean of a binomial distribution is always greater than the variance.

(B) The mean of a Poisson distribution is always greater than the variance.

(C) If $f(x)$ is the probability density function of a random variable $X$ , then $P(a \leq X \leq b) = \int_a^b f(x)dx$ .

(D) If $X$ is a random variable and $a,b$ are real numbers, then $Var(aX+b)=a^2Var(X)$ .

Choose the correct answer from the options given below:

2022: 25 May Shift 1

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is

For 6 trials of an experiment, let X be a binomial variate which satisfies the relation 9P(X=4)=P(X=2)9P(X=4)=P(X=2)9P(X=4)=P(X=2), then the probability of success is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

For 6 trials of an experiment, let X be a binomial variate which satisfies the relation $9P(X=4)=P(X=2)$ , then the probability of success is