Probability practice · Easy

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

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

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

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

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

In a binomial distribution $B(n, p=1 / 4)$ If the probability of at least one success is greater than or equal to $9 / 10$, then $n$ is greater than

$n$ persons are seated on $n$ chairs at a round table. The probability that two specified persons are sitting next to each other, is

Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then, $P(X = 1) + P(X = 2)$ equals

Three integers are chosen at random without replacement from the first 20 integers. The probability that their product is even is

An experiment succeeds twice as often as it fails. The probability that in the next six trials there are at least 4 successes, is

In a series of three trials the probability of exactly two successes in nine times as large as the probability of three successes. Then, the probability of success in each trial is

$A,B,C$ are any three events. If $P\left( S \right)$ denotes the probability of $S$ happening, then $P\left( {A \cap \left( {B \cup C} \right)} \right) =$

Let $X$ have a binomial distribution $B(n, p)$ such that the sum and the product of the mean and variance of $X$ are 24 and 128 respectively. If $P(X>n-3)=$ $\frac{k}{2^n}$, then $k$ is equal to :

In a group of people, if 4 are selected at a random, the probability that the any two of the four do not have same month of birth is $p$ then $\frac{96 p}{11}$ is equal to

A bag contains 100 tickets numbered 1 to 100. If one ticket is picked up at random, then the probability that the number is divisible by 3 or 5 is

A 7-digit number is formed using the digit 4 three times, digit 5 two times and digit 3 two times. A number is chosen at random, the probability that the chosen mumber is even, is

If the mean and variance of a variate $X$ having a binomial distribution are 6 and 4 respectively. then the number of values of the variate in the distribution is

If ${X}$ follows a binomial distribution with parameters $n$ $=8$ and $p=1 / 2$, then ${P}(|{X}-4| \leq 2)=$