Algebra

Probability

Easy

In Binomial distribution with parameters $n = 100$ and p, Variance of distribution is maximum when p is equal to :

$\frac{1}{100}$

$\frac{1}{50}$

$\frac{1}{2}$

$\frac{1}{200}$

✅ Correct Option: 3

Variance of Binomial $= npq = np(1-p)$ .

For fixed $n$ , $V(p) = np(1-p)$ . $V'(p) = n(1 - 2p) = 0 \Rightarrow p = \frac{1}{2}$ .

$V''(p) = -2n < 0$ , so maximum at $p = \frac{1}{2}$ .

2022: 17 Aug Shift 2

It is given that only 0.1% of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :

For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.

Based on the above informations, answer the question :

The probability that the selected person will be diagonosed as COVID positive is :

2025: 3 June Shift 2

The binomial distribution for which the mean is 5 and variance 4, is

2025: 19 May Shift 1

Match List-I with List-II

Let A and B be any two events

List-I	List-II
(A) $P(A')$	(I) $\frac{P(A \cap B)}{P(A)}; P(A) \neq 0$
(B) $P(\phi)$	(II) $\frac{P(A \cap B)}{P(B)}; P(B) \neq 0$
(C) $P(A\vert B)$	(III) $1 - P(A)$
(D) $P(B\vert A)$	(IV) 0

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

A card is picked at random from a pack of 52 playing cards. If the picked card is a queen, then probability of card to be of spade type also, is

2026: 31 May Shift 2

If $A$ and $B$ are two events such that $P(\overline{A} \cup \overline{B}) = \dfrac{2}{3}$ and $P(A \cup B) = \dfrac{5}{9}$ , then which of the following are TRUE?

A. $P(A \cap B) = \dfrac{1}{3}$

B. $P(A \cup B) + P(A \cap B) = \dfrac{7}{9}$

C. $P(A) + P(B) = \dfrac{2}{9}$

D. $P(\overline{A}) + P(\overline{B}) = \dfrac{10}{9}$

Choose the correct answer from the options given below:

2025: 16 May Shift 1

In class XII, suppose 5% of boys and 0.25% of girls are physically fit for a game. A fit student is selected at random from this class having same number of boys and girls. If the probability that the selected student is a girl is $\frac{m}{n}$ , gcd(m, n) = 1, then m + n is equal to

In Binomial distribution with parameters n=100n = 100n=100 and p, Variance of distribution is maximum when p is equal to :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

In Binomial distribution with parameters $n = 100$ and p, Variance of distribution is maximum when p is equal to :