Probability practice · Mixed difficulty

Probability of throwing 16 in one throw with three dice is

${A}, {B}$ and ${C}$ are three mutually exclusive and exhaustive events. If $\frac{1}{3} {P}({C})=\frac{1}{2} {P}({A})={P}({B})$, then ${P}({B})=$

10 persons sit around a circular table with 10 numbered chairs. The probability that the two particular persons $A$ and $B$ are always together is

One Indian and four American men and their wifes are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

If the range of a random variable $X$ is {0,1,2,3,4,…} with $P\left( {X = k} \right) = \frac{{\left( {k + 1} \right)a}}{{{3^k}}}$ for $k \ge 0,$ then $a$ is equal to

Probability of all 3 digit numbers having all the digits same is

For two events $A$ and $B$, if $P\left( A \right) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}$ and $P\left( {\frac{B}{A}} \right) = \frac{1}{2},$ then

A random variable X takes values $-1,0,1,2$ with probabilities $\frac{1+3 p}{4}, \frac{1-p}{4}, \frac{1+2 p}{4}, \frac{1-4 p}{4}$ respectively, where $p$ varies over $R$. Then the minimum and maximum values of the mean of $X$ are respectively

Two integers $x$ and $y$ are chosen with replacement out of the set $\{0,1,2,3, \ldots, 10\}.$ Then the probability that $|x-y|>5,$ is

The odds in favour of a book reviewed by three independent critics are, respectively, $5: 2,4: 3$ and $3: 4$. The probability that majority of the critics give favourable remark is

A die is tossed thrice. A success is getting 1 or 6 on a toss. The mean and the variance of number of successes

$\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \ldots \ldots \mathrm{x}_{50}$ are fifty real numbers such that $x_r < x_{r+1}$ for $r=1,2,3, \ldots .49$. Five numbers out of these are picked up at random and they are arranged in increasing order. The probability that the five numbers have $x_{20}$ as the middle number is :

A contest consists of predicting the results (win, draw or defeat) of 10 football matches. The probability that one entry contains at least 5 correct answers is

Two persons each make a single throw with a pair of dice. The probability that the throws are equal, is

A coin is tossed three times. The probability of getting head and tail alternatively, is

A man and his wife appear for an interview for two posts. The probability of the man’s selection is 1/5 and that of his wife’s selection is 1/7. The probability that at least one of them is selected, is

A die is tossed twice. The probability of having a number greater than 4 on each toss is

A bag A contains 2 white and 3 red balls, and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and it is found to be red. Let $p$ be the probability that it was drawn from the bag B then find the value of $\left[\frac{1}{p}\right]$ where [.] denotes G.I.F.

If three students $A,\,B,\,C$ can solve a problem with probabilities $\frac{1}{3},\,\frac{1}{4}$ and $\frac{1}{5}$ respectively, then the probability that the problem will be solved is

Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^N < N !$ is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $4 m-3 n$ is equal to

Three persons, A, B and $\mathrm{C}$, fire at a target in turn, starting with $\mathrm{A}$. Their probability of hitting the target are $0.4,0.3$ and 0.2 respectively. The probability of two hits is

A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss, equals

If $n$ integers taken at random are multiplied together, then the probability that the last digit of the product is 1, 3, 7 or 9, is

The probability of getting the sum more than 7 when a pair of dice is tossed is

$'X'$ speaks truth in 60% and $'Y'$ in 50% of the cases. The probability that they contradict each other narrating the same incident is

Two coins and a die are tossed. The probability that both coins fall heads and the die shows a 3 or 6, is

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{k}{2^{15}}$, then $k$ is equal to

The probability that in a family of 5 members, exactly 2 members have birthday on sunday, is

Let a die is loaded in such a way that prime number faces are twice as likely to occur as a non-prime number faces. Then, the probability that an odd number will be show up when the die is tossed, is