Applied Mathematics

Probability Distribution

Medium

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 :

$1 - \left(\frac{9}{10}\right)^9$

$\frac{9}{10}$

$1 - \left(\frac{9}{10}\right)^{10}$

$1 - \frac{10^9}{10^{10}}$

✅ Correct Option: 3

Let $X$ = number of defective bulbs in 10 draws. $p = 0.1, q = 0.9, n = 10$ . P(at least one defective) $= 1 - P(X = 0) = 1 - \binom{10}{0} (0.9)^{10} = 1 - \left(\frac{9}{10}\right)^{10}$ .

2026: 21 May Shift 2

A random variable X follows Poisson distribution. The variance of X is 2. The value of $P(X=3)$ is

2023: 11 Aug Shift 1

The probability distribution of a discrete random variable X is given by :

X	30	10	-10
P(X)	1/5	3/10	1/2

then E(X) is equals to

2026: 26 May Shift 2

In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE?

A. The number of trials is infinite.

B. Each trial has exactly two outcomes defined as success and failure.

C. The trials are dependent by nature.

D. The probability of success remains the same in each trial.

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

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:

2026: 21 May Shift 2

In a single throw of a die, if X denotes the number on its upper face, then the mean of X is,

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 :

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)