CUET Mathematics: Applied MathematicsProbability Distribution. Free, no login required.

There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

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

A box containing 10 wall clocks has three defective pieces in it. If random sample of two clocks is taken from the box, then the probability distribution of defective clocks is:

On a multiple choice examination with four possible answers (out of which only one is correct) for each of five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

The number of telephone calls made daily in a certain community between 8 P.M. and 9 P.M. has a mean of 352 and standard deviation of 31. What percentage of time will there be more than 400 telephone calls made in this community between 8 P.M. to 9 P.M.?

[Given that: $P(0\leq Z\leq1.55)=0.4394$, where $Z$ is the standard normal variate]

A box contains 8 red and 2 white balls. If three balls are drawn, one by one, at random without replacement, then the variance of the number of white balls drawn is:

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$]

In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

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

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

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

A random variable X has the following probability distribution:

Which of the following are correct?

(A) $P(X \le 1)=0.25$

(B) $P(X>3)=0.15$

(C) $P(X=2)=0.30$

(D) $P(X \le 2)=0.55$

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If X is a Poisson variate such that $3P(X=2)=2P(X=1)$, then $P(X=0)$ is equal to: (Given $e^{-4/3}=0.264$)

Let X denote the number of scores in a test. If X is normally distributed with mean 100 and standard deviation 15, then the probability that X does not exceed 130 is,

(Given $P(0 \le Z \le 2)=0.4772$, where $Z$ be the standard normal variate)

A traffic police officer records the number of motorcycle riders that use a particular lane on a highway. He records that an average of 2.5 motorcycle riders use the lane every hour. Given that the number of motorcycles that use the particular lane follows a Poisson distribution. The probability that less than 2 motorcycle riders will use the lane within an hour will be:- (Use $e^{2.5} = 12.2$)

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.

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If $X$ is a random variable such that $X$ can take values 0,1, 2 or 3. Then the expectation of $X$ for the following data is :

(where $k>0$)

If a random variable X follows poisson's distribution such that $P(X=2) = 9P(X=4) + 90P(X=6)$, then the mean of X is

The mean and variance of a random variable $X$ having a binomial distribution are 1 and 2/3 respectively. Then,

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If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$.

If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$, then which of the following are TRUE?

A. $P(X=1) = \dfrac{1}{13}$

B. $P(X=3) = \dfrac{1}{13}$

C. $E(X) = \dfrac{18}{13}$

D. $P(X=2) = \dfrac{6}{13}$

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If the heights of 300 students are normally distributed with mean 68 inches and standard deviation 3 inches. If Z is the standard normal variate such that $P(0\le Z\le 1.33)=0.4082, P(Z\ge 1.33)=0.0918$ and $P(0\le Z\le 1)=0.3413$, then which of the following statements are correct?

(A) There are 27 students whose height is greater than 72 inches.

(B) The number of students having heights less than or equal to 64 inches is 27.

(C) 210 students have their heights between 65 and 71 inches.

(D) There are 35 students whose height is greater then 72 inches.

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

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

If a random variable X follows binomial distribution with mean $\dfrac{4}{3}$ and variance $\dfrac{8}{9}$. Which of the following are correct?

A. Probability of success is $\dfrac{1}{3}$.

B. Probability of failure is $\dfrac{2}{3}$.

C. Number of trials is 4.

D. $P(X \ge 1) = \dfrac{35}{81}$

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

The random variable X has a probability distribution $P(X)$ of the following form, where $k$ is some real number.

$P(X=x) = \begin{cases}k, & \text{if } x=0\\\dfrac{k}{2}, & \text{if } x=1 \text{ or } 2\\0, & \text{otherwise}\end{cases}$

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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

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If $X$ is a discrete random variable which assumes values $x_1, x_2, x_3, ..., x_n$ with the respective probabilities $p_1, p_2, ....., p_n$, then

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

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

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