List of top Mathematics Questions on Probability Distribution

Consider the random experiment of throwing a die and tossing a coin. Let \[ \{(a,b)\mid a\in\{H,T\},\ b\in\{1,2,\ldots,6\}\} \] denote the outcomes of the experiment. If $X$ is a random variable defined by \[ X(a,b)=b, \] then the variance of $X$ is
If $X\sim B(n,p)$ is a binomial variate, $8p^2+15p-2=0$ and the product of the mean and variance of $X$ is $\dfrac78$, then $P(X=4)=$
A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is:
In a binomial distribution, the mean is 4 and the variance is 3. Then the number of trials $n$ is:
If X is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$, $k=0,1,2,\dots,\infty$, then $P(X=3) =$
Functions are formed from the set $A = \{a_1, a_2, a_3\}$ to another set $B = \{b_1, b_2, b_3, b_4, b_5\}$. If a function is selected at random, the probability that it is a one-one function is
A and B are two events of a random experiment such that $P(B)=0.4$, $P(A \cap \bar{B}) = 0.5$, $P(A \cup B) + P(A|B) = 1.15$, then $P(A)=$
In a Poisson distribution, if $\frac{P(X=5)}{P(X=2)} = \frac{1}{7500}$ and $\frac{P(X=5)}{P(X=3)} = \frac{1}{500}$, then the mean of the distribution is
In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three times by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is
There are two boxes each containing 10 balls. In each box, few of them are black balls and rest are white. A ball is drawn at random from one of the boxes and found that it is black. If the probability that the black ball drawn is from the second box is $\frac{1}{5}$, then number of black balls in the first box is
Three companies C1, C2, C3 produce car tyres. A car manufacturing company buys 40% of its requirement from C1, 35% from C2 and 25% from C3. The company knows that 2% of the tyres supplied by C1, 3% by C2 and 4% by C3 are defective. If a tyre chosen at random from the consignment received is found defective then the probability that it was supplied by C2 is
The probability distribution of a random variable X is given below. Then, the standard deviation of X is.
If the mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{10}{9}$ respectively, then $P(X \geq 6) =$
If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is
Out of the given 25 consecutive positive integers, three integers are drawn. If the least integer among given 25 integers is an odd number, then the probability that the sum of the three integers drawn is an even number is
If a Poisson variate X satisfies the relation $P(X=3) = P(X=5)$, then $P(X=4) =$
Two cards are drawn randomly from a pack of 52 playing cards one after the other with replacement. If A is the event of drawing a face card in the first draw and B is the event of drawing a clubs card in the second draw, then $P\left(\frac{B}{A}\right)=$
If a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively is
If a number x is drawn randomly from the set of numbers \{1, 2, 3, ..., 50\}, then the probability that number x that is drawn satisfies the inequation $x + \frac{10}{x} \le 11$ is
A random variable \( X \) has the following probability distribution:

X012otherwise
P(X)k2k3k0

Then: 
(A) \( k = \frac{1}{6} \) 
(B) \( P(X < 2) = \frac{1}{2} \) 
(C) \( E(X) = \frac{3}{4} \) 
(D) \( P(1 < X \leq 2) = \frac{5}{6} \) 
Choose the correct answer from the options given below:

A random variable \( X \) has the following probability distribution:
X01234567
P(X)0m2m2m3mm²2m²7m² + m
The value of m is:
A random variable X has the following probability distribution:
X1234567
P(X)k2k2k3kk22k27k2 + k

Match the options of List-I to List-II:
List-IList-II
(A) k(I) 7/10
(B) P(X < 3)(II) 53/100
(C) P(X ≥ 2)(III) 1/10
(D) P(2 < X ≤ 7)(IV) 3/10

Choose the correct answer from the options given below.
If the random variable X has the following distribution:
X012otherwise
P(X)k2k3k0

Match List-I with List-II:
Table
Choose the correct answer from the options given below:
For the following probability distribution:
X345
P(X)0.50.20.3
The mean, variance, and standard deviation respectively are:

It is known that 20% of the students in a school have above 90% attendance and 80% of the students are irregular. Past year results show that 80% of students who have above 90% attendance and 20% of irregular students get “A” grade in their annual examination. At the end of a year, a student is chosen at random from the school and is found to have an “A” grade. What is the probability that the student is irregular?