Probability PYQs - Last 5 Years

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Practice 102 TS EAMCET Mathematics questions from Probability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Probability Questions

Showing 50 of 102 filtered questions.

Let $A$ and $B$ be two events in a random experiment . If $P(A \cap \bar{B})=0.1, P(\bar{A} \cap B)=0.2$ and $P(B)=0.5$, then $P(\bar{A} \cap \bar{B})=$

An urn contains 7 red, 5 white and 3 black balls. Three balls are drawn randomly one after the other without replacement. If it is known that first ball drawn is red and the second ball drawn is white, then the probability that the third ba...

If two smallest squares are chosen at random on a chess board, then the probability of getting these squares such that they do not have a side in common is

Among every 8 units of a product, one is likely to be defective. If a consumer has order 5 units of that product, then the probability that atmost one unit is defective among them is

The range of a discrete random variable $X$ is $\{1,2,3\}$ and the probabilities of its elements are given by $P(X=1)=3 k^3, P(X=2)=2 k^2$ and $P(X=3)=7-19 \mathrm{k}$. Then, $P(X=3)=$

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 ...

In possion 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

$A$ and $B$ are two events of a random experiment such that $P(B)=0.4, P(A \cap \bar{B})=0.5, P(A \cup B)+P\left(\frac{B}{A \cup \bar{B}}\right)=1.15$ then $P(A)=$

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three time by replacing the book already taken every time, then the mean of the number of mathematics book...

Functions are formed from the set $A=\left\{a_1, a_2, a_3\right\}$ to another set $B=\left\{b_1, b_2, b_3, b_4, b_5\right\}$. If a function is selected at random, then probability, that it is a non-one function is

If a coin is tossed seven times, then the probability of getting exactly three heads such that number two heads occur consecutively is

If $X$ is a random variable with probability distribution $P(X=k)=\frac{(2 k+3) c}{3^k}, k=0,1,2, \ldots .$. to $\infty$, then $P(X=3)=$

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 first draw and $B$ is the event of drawing a clubs card in second draw, then $P\left(\frac{\bar...

If a number $x$ is drawn randomly from the set of numbers $\{1,2,3, \ldots ., 50\}$, then the probability that number $x$ that is drawn satisfies the inequation $x+\frac{10}{x} \leq 11$ is

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

Three companies $C_1, C_2, C_3$ produce car tyres. A car manufacturing company buys $40 \%$ of its requirement from $C_1, 35 \%$ from $C_2$ and $25 \%$ from $C_3$. The company knows that $2 \%$ of the tyres supplied by $C_1, 3 \%$ by $C_2$ ...

Out of the given 25 consecutive position 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 the mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{10}{9}$ respectively, then $P(X \geq 6)=$

Urn A contains 6 white and 2 black balls; run B contains 5 white and 3 black balls and urn C contains 4 white and 4 black balls. if an urn is chosen at random and a ball is drawn at random from it, then the probability that the ball drawn i...

If three cards are drawn randomly from a pack of 52 playing cards then the probability of getting exactly, one spade card, exactly one king and exactly one card having a prime number is

If three smallest squares are chosen at-random on a chess board, then the probability of getting them in such a way that they are all together in a row or in a column is

$A, B$ are the events in a random experiment.
If $P(A)=\frac{1}{2}, P(B)=\frac{1}{3}, P(A \cap B)=\frac{1}{4}$, then $P\left(\frac{A^c}{B^c}\right)+P\left(\frac{A}{B}\right)=$

Let $P=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ be a matrix. Three elements of this matrix $P$ are selected at random. $A$ is the event of having the three elements whose sum is odd. $B$ is the event of...

A typist claims that he prepares a typed page with typo errors of 1 per 10 pages. In a typing assignment of 40 pages, if the probability that the typo errors are at most 2 is $p$, then $e^2 p=$

$A, B_1, B_2, B_3$ are the events in a random experiment. If $P\left(B_1\right)=0.25, P\left(B_2\right)=0.30, P\left(B_3\right)=0.45, P\left(\frac{A}{B_1}\right)=0.05$, $P\left(\frac{A}{B_2}\right)=0.04, P\left(\frac{A}{B_3}\right)=0.03$, t...

Two persons $A$ and $B$ play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even, A will get $\frac{1}{2}$ point and $B$ will get $\frac{1}{2}$ point.
If the sum is odd, A will get one point and $B$ will ...

If the probability that a student selected at random from a particular college is good at mathematics is 0.6 , then the probability of having two students who are good at Mathematics in a group of 8 students of that college standing in fron...

If on an average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in a specific hour is

If 2 cards are drawn at random from a well shuffled pack of 52 playing cards from the same suit, then the probability of getting a face card and a card having a prime number is

When 2 dice are thrown, it is observed that the sum of the numbers appeared on the top faces of both the dice is a prime number. Then, the probability of having a multiple of 3 among the pair of numbers thus obtained is

A dealer gets refrigerators from 3 different manufacturing companies $C_1, C_2$ and $C_3 .25 \%$ of his stock is from $C_1, 35 \%$ from $C_2$ and $40 \%$ from $C_3$. The percentages of receiving defective refrigerators from $C_1, C_2$ and $...

Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from ur...

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of the dice is

If a random variable X has the following probability distribution, then the mean of $X$ is

$$ \begin{array}{c|c|c|c|c} X=x_1 & 1 & 2 & 3 & 5 \\ \hline p\left(X=x_i\right) & 2 k^2 & k & k & k^2 \end{array} $$

If a random variable $X$ has the following probability distribution, then its variance is .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-si...

The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. IfP $(X > 1)=1-K\left(\frac{3}{5}\right)^{7}$, then $5 K=$

The numbers $2,3,5,7,11,13$ are written on six distinct paper chits. If 3 of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by 3 , is

If two dice are rolled, then the probability of getting a multiple of 3 as the sum of the numbers appeared on the top faces of the dice, if it is known that their sum is an odd number, is

Bag $P$ contains 3 white, 2 red, 5 blue balls and bag $Q$ contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random, then the probability that it is a red bal...

If two dice are thrown, then the probability of getting co-prime numbers on the dice is

If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a cards having a composite number and a card having a number which is a multiple of 3 is

If the probability distribution of a random variable $X$ is as follow, then the variance of $X$ is

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A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PRO...

Two cards are drawn at random one after the other with replacement from a pack of playing cards. If $X$ is the random variable denoting the number of ace cards drawn, then the mean of the probability distribution of X is

If three numbers are randomly selected from the set $\{1,2,3, \ldots \ldots 50\}$, then the probability that they are in arithmetic progression is

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that first three tosses resulted in 2 or more heads is

A random variable $X$ has the following probability distribution
$$ \begin{array}{|c|l|l|l|l|l|l|l|l|} \hline \boldsymbol{X}=\boldsymbol{x} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & 0.15 & 0.2...

5 persons entered a lift cabin in the cellar of a 7 floor building apart from cellar. If each of them independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probabili...