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.

A bag contains four balls. Two balls are drawn randomly and found them to be white. The probability that all the balls in the bag are white is

If the coefficients $a$ and $b$ of a quadratic expression $x^2+a x+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1,2,3,4\}$ respectively, then the probability that the equation $x^2+a x+b=0$ has real roots is

There are 10 coins in a box out of which 8 are normal and the remaining are with heads on both sides. A coin is chosen at random from the box and tossed 6 times. If it shows heads each time, then the probability that the selected coin has h...

A boy throws an unbiased die. Whenever he gets 1 on the die he has a further chance to throw it once again immediately. The probability that the boy gets a score of 7 in this process is

\(\text { A random variable } X \text { has the following distribution, }\)
$$ \begin{array}{lllllll} \hline X=x_i & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline P\left(X=x_i\right) & 0.1 & k & 0.2 & 2 k & 3 k & k \\ \hline \end{array} $$
Then, the ...

If a matrix is chosen at random from the set of all $3 \times 3$ non-zero matrices whose entries are the elements of the set $\{-1,0,1\}$, then the probability that the matrix is skew-symmetric is

If three unbiased dice are rolled simultaneously, then the probability that all the three dice show distinct numbers is

If two cards are drawn at random simultaneously from a pack of 52 playing cards, then the probability of getting a face card and a spade card other than the face card is

Two cards are drawn at random one after the other with replacement from a pack of 52 playing cards. Then, the variance of the random variable of the number of spade cards among the drawn cards is

Three persons $A, B$ and $C$ attended a recruitment test, The ratio of the chances of $A, B, C$ in getting through the test is $1: 2: 3$ and their probabilities to face the interview successfully are $0.8,0.7,0.6$, respectively. If one of t...

In a game, two dice are thrown simultaneously by a person $A$ and two cards are drawn at random simultaneously from a pack of 52 playing cards by a person $B$. They win the game, if $A$ gets a prime score as the sum of the numbers appear on...

A bag contains 3 red, 5 black and 7 blue balls. If three balls are drawn at random simultaneously from the bag, then the probability of getting at least two blue balls is

Two players $A$ and $B$ alternatively toss 3 coins simultaneously. The player who gets 2 heads and 1 tail first, wins the game. If game continues until someone wins and if $A$ begins the game, the probability that B wins the game is

If $P(X=x)=c\left(\frac{2}{3}\right)^x ; x=1,2,3,4, \ldots$ is a probability distribution function of a random variable $X$, then the value of $c$ is

The equation of the parabola with $x+2 y=1$ as directrix and $(1,0)$ as focus is

If $A$ and $B$ are two events in a random experiment such that $P(A)+P(B)=2 P(A \cap B)$, then

In a non-leap year, the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is

A student is given 6 questions in an examination with true or false type of answers. If he writes 4 or more correct answers, he passes in the examination. The probability that he passes in the examination is

If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is

Two bad eggs are mixed accidentally with 10 good ones. If three eggs are drawn at random from this lot in succession without replacement, then the variance of the probability distribution of the number of bad eggs drawn is

If $A$ and $B$ are two events of a random experiment such that $P(A \cup B)=P(A \cap B)$, then which one amongst the following four options is not true?

$A, B, C, D$ cut a pack of 52 well shuffled playing cards successively in the same order. If the person who cuts a spade first, wins the game and the game continues until this happens, then the probability that $A$ wins the game is

A bag contains 9 identical black balls numbered 1 to 9 . and 4 identical white balls numbered 1 to 4 . If 3 balls are drawn at a time randomly from that bag, then the probability of getting atleast one white ball is

When 3 dice are thrown at a time, the sum of the numbers appeared on 3 dice were found to be 15 . Then, the probability that the number 5 does not appear on any one of the dice is

If the probability distribution of a random variable $X$ is given by
$$ \begin{array}{|c|c|c|c|c|c|c|} \hline X=x & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline P(X=x) & 0 & k & 2 k & 5 k^2 & 2 k^2 & 3 k \\ \hline \end{array} $$
then the mean of $X$ is

The probability of getting a success in a trail is five times that of a failure. The probability of getting atmost one success in 5 trails, is

The probabilities of two persons to hit a target are $1 / 4$ and $1 / 5$ respectively. The probability that the target is being hit when both of them attempt independently is

Bag $A$ contains 4 white and 2 black balls, bag $B$ contains 3 white and 3 black balls and bag $C$ contains 2 white and 4 black balls. If a bag is chosen at random and a ball is chosen at random from it, then the probability that the ball d...

If $X$ is a Poisson variate such that $\frac{5}{3} k=P(X=2) =P(X=3)$, then $P(X=5)=$

The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of 52 playing card is

Two cards are drawn from a pack of 52 playing cards one after the other. If $p_1$ is the probability of getting a queen in the first draw and a diamond card in the second draw when the first card drawn is replaced and $p_2$ is the probabili...

A random variable $X$ has the following probability distribution
$$ \begin{array}{llllllllll} \hline X=\mathbf{x}_i & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline P\left(X=\mathbf{x}_i\right) & 10 k & 9 k & 8 k & 8 k & 6 k & 5 k & 4 k & 3 k ...

In an experiment a person gets success $\alpha$ times out of $\beta$ trails. If the experiment consists of $n$ trials, then the probability that he fails at least $(n-1)$ times is

A random variable $X$ has the range $\{0,1,2, \ldots$.$\} . If P(X=r)=k(1+r) 3^{-r}$, for $r=0,1,2, \ldots$ where $k>0$ is a real number, then $P(X=0)+P(X=1)+P(X=2)=$

If $A$ and $B$ are two events of a random experiment such that $P(\bar{A})=\frac{2}{3}, P(B)=\frac{4}{15}$ and $P(A \cap \bar{B})=\frac{1}{5}$, then $\sqrt{195[P(B \mid(A \cup \bar{B}))+P(A \cup B)]}=$

If two cards are drawn simultaneously from a well shuffled pack of 52 cards, then the probability of getting a card having a prime number and a card having a number which is a multiple of 5 is

When two dice are thrown, the probability of getting an ordered pair $(x, y)$ such that $x^2+y^2 \leq 25$ where $x$ and $y$ are numbers that show up on the two dice, is

Two players $A$ and $B$ are alternately throwing a coin and a die together. $A$ player who first throws head and 6 wins the game. If $A$ starts the game, then the probability that $B$ wins the game is

If two dice are thrown and if $X$ denotes the sum of the numbers that show up on the faces of the dice, then the mean of the random variable $X$ is

A bag contains 3 white and 6 red balls. Four balls are drawn at a time randomly. Then, the probability of getting at least two red balls is

In a university campus, the probability that a person chosen at random is an engineering student is $\frac{1}{5}$. The probability of having atmost two engineering students in a sample of 8 people is

$A$ and $B$ are two independent events $P(A)=\frac{2}{5}, P(B)=\frac{1}{3}$.
Match the following :

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A cube having edge of length 5 cm is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also...

If the mean and variance of a binomial distribution are 4 and $\frac{4}{3}$ respectively, then $P(X=2)=$

Two balls are drawn at random from a bag containing 5 black balls and 3 white balls. If the random variable $X$ denotes the number of white balls drawn, then the mean of $X$ is

A pair of dice is thrown twice in succession. The probability of getting prime number on both the dice in first throw and composite numbers on both the dice in second throw is

3 balls are drawn one after the other without replacement from an urn containing 4 red, 5 blue and 6 yellow balls. The probability of getting three different coloured balls is

Let $A, B, C$ be three pairwise independent events of a random experiment. If $P(\bar{B} \cup \bar{C})=\frac{1}{2}, P(A)>0, P(B)=b$ and $P(C)=c, P((\bar{B} \cap \bar{C} \mid A)=$

When two dice are thrown, the probability of getting a prime number on die and a composite number on the other is

In a random experiment of throwing 5 coins, the number of heads is defined as a random variable. The mean of the random variable is