Probability practice · Mixed difficulty

A five-digit number (having all different digits) is formed using the digits $1,2,3,4,5,6,7,8$ and 9. The probability that the formed number either begins or ends with an odd digit, is equal to:

4 five-rupee coins, 3 two-rupee coins and 2 one-rupee coins are stacked together in a column at random. The probability that the coins of the same denominator are consecutive is

A binomial variate $\mathrm{X}$ has mean $=6$ and variance $=2$ the probability that $5 \leq \mathrm{X} \leq 7$ is

A sum of money is rounded off to the nearest rupee. The probability that round off error is at least ten paise is

The probability that A speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is

The probability that the triangle formed by choosing any three vertices from the vertices of a cube is equilateral is

Five horses are in a race. Mr. $A$ selects two of the horses at random and bets on them. The probability that Mr. $A$ selected the winning horse, is

The random variable $X$ follows binomial distribution $B(n, p)$, for which the difference of the mean and the variance is 1 .

If $2 P(X=2)=3 P(X=1)$, then $n^{2} P(X>1)$ is equal to

Let $A$ and $B$ be two events such that $P(A)=0.3$ and $P(A \cup B)=0.8$. If $A$ and $B$ are independent events, then $P(B)=$

In order to get at least once a head with probability $\ge 0.9,$ the number of times a coin needs to be tossed is

A die is thrown. Let $A$ be the event that the number obtained is greater than 3. Let $B$ be the event that the number obtained is less than 5. Then $P\left( {A \cup B} \right)$ is

$A$ and $B$ are two independent witnesses (ie, there is no collusion between them) in a case. The probability that $A$ will speak the truth is $x$ and the probability that $B$ will speak the truth is $y$, $A$ and $B$ agree in a certain statement. The probability that the statement is true, is

Given $P\left( A \right) = 0.5,\;P\left( B \right) = 0.4,\;P\left( {A \cap B} \right) = 0.3,$ then $P\left( {\frac{{A'}}{{B'}}} \right)$ is equal to

Consider the experiment of rolling a die. Let ${A}$ be the event 'getting a prime number' and $B$ be the event 'getting an odd number'.

Then, which of the following is true?

I. ${A}$ or ${B}={A} \cup {B}=\{1,2,3\}$

II. ${A}$ and ${B}={A} \cap {B}=\{3,5\}$

III. ${A}$ but not ${B}={A}-{B}=\{2\}$

IV.Not ${A}={A}^{\prime}=\{1,5,6\}$

Two dice are thrown. The Probability that the number appeared have a sum 8 if it is known that the second dice always exhibits 4 , is

A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is

A box conatins $2 n$ cards numbered $2^0, 2^1$, $2^2, \ldots, 2^{2 n-1}$. Two cards are taken out at random from the box, at random without replacement. Probability that sum of the numbers on the card is divisible by 3 is

Six boys and six girls sit in a row randomly. The probability that all the six girls sit together is

The probability that the two digit number formed by digit 1, 2, 3, 4, 5, is divisible by 4 (while repetition of digit is allowed), is

A number $n$ is chosen at random from $S = \left\{ {1,\;2,\;3,\; \ldots ,\;50} \right\}.$
Let $A = \left\{ {n \in S:n + \frac{{50}}{n} > 27} \right\},\;B = \left\{ {n \in S:n\;\mathrm{is\;a\;prime}} \right\}$ and $C = \left\{ {n \in S:n\;\mathrm{is\;a\;square}} \right\}.\mathrm{\;}$Then, correct order of their probabilities is

A letter is chosen at random from the word 'ASSASSINATION'.

I. The probability that letter is a vowel is $\frac{6}{13}$.

II. The probability that letter is a consonant is $\frac{7}{13}$.

One of the two events must happen. Given that the chance of one is two-third of the other, the odds in favour of the other are

A boy is throwing stones at a target. The probability of hitting the target at any trial is $1 / 2$. The probability of hitting the target 5th time at the 10th throw is

A die has four blank faces and two faces marked 3. The change of getting a total of 12 in 5 throws is

The probability that a man who is 85 years old will die before attaining the age of 90 is $1 / 3$. Four persons $A_1, A_2, A_3$ and $A_4$ are 85 years old. The probability that $A_1$ will die before attaining the age of 90 and will be the first to die is

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

A man takes a step forward with probability 0.4 and backward with probability 0.6 . The probability that at the end of eleven steps he is one step away from the starting point is

Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets got to daughters of $A$ is 1/20. The number of daughters each of them have is

A box contains 4 white and 5 black balls. $A$ ball is drawn at random and its colour is noted. A ball is then put back in the box along with two additional balls of its opposite colour. If a ball is drawn again from the box, then the probability that the ball drawn now is black, is

$A$ and $B$ toss a coin alternately till one of them tosses heads and wins the game, their respective probability of winning are