Probability practice · Mixed difficulty

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 houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house, is

Two marbles are drawn in succession from a box
containing 10 red, 30 white, 20 blue and 15 orange
marbles, with replacement being made after each
drawing. Then the probability, that first drawn
marble is red and second drawn marble is white, is

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

If from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn, 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 $P\left( {A \cap \left( {B \cup C} \right)} \right) =$

A dice is weighted such that the probability of rolling $\mathrm{n}$ is proportional to $\mathrm{n}^2(\mathrm{n}=1,2,3,4,5,6)$. The dice is rolled twice, yielding the numbers a and $\mathrm{b}$. The probability that $\mathrm{a}<\mathrm{b}$ in lowest form is $\frac{\mathrm{p}}{\mathrm{q}}$ where $\frac{620}{(\mathrm{p}+\mathrm{q})}=$

Let $S=\left\{w_1, w_2, \ldots \ldots\right\}$ be the sample space associated to a random experiment. Let $P\left(w_n\right)=\frac{P\left(w_{n-1}\right)}{2}, n \geq 2$. Let $A=\{2 k+3 l: k, l \in N\}$ and $B=\left\{w_n: n \in A\right\}$. Then $P(B)$ is equal to

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

Three persons $A, B, C$ throw a die in succession. The one getting 'six' wins. If $A$ starts then the probability of $B$ winning 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 ${P}(|{X}-4| \leq 2)=$

The probability that out of 10 persons, all born in June, at least two have the same birth day is

An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed, is

Three numbers are chosen at random (without replacement) from the numbers $1,2, \ldots 20$. The probability that the numbers are not consecutive are

If two coins are tossed five times, then the probability of getting 5 heads and 5 tails is

The mode of the binomial distribution for which mean and standard deviation are 10 and $\sqrt 5 \;$ respectively, is

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to through 9 from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins the game, is

If the letters of the word PROBABILITY are written down at random in a row, the probability that two Bs are together is

If $\frac{1-3 p}{2}, \frac{1+4 p}{3}, \frac{1+p}{6}$ are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of $p$ is

A card is drawn from a pack of cards. The probability that the card will be a queen or a heart, is

Which one of the following is not correct?

All the heart cards are taken out from a pack of playing cards. From these cards, cards are drawn one by one without replacement till the ace of hearts comes. The probability that ace comes in the 4th draw is