Probability practice · Mixed difficulty

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is

A random variable $X$ takes values 0, 1, 2, 3,… with probability $P\left( {X = x} \right) = k\left( {x + 1} \right){\left( {\frac{1}{5}} \right)^x},$ where $k$ is constant, then $P\left( {X = 0} \right)$ is

A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears, is

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

If $\mathrm{A}$ and $\mathrm{B}$ are independent events, then which of the following is not true?

India play two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1 and 2 are $0.45,0.05$ and $0.50$, respectively. Assuming that the outcomes are independent, then the probability of India getting atleast 7 points, is

If $A$ and $B$ are two mutually exclusive events, then

A die is rolled three times, if $p$ be the probability of getting a large number than the previous number, then the value of $54 p$ is

Three numbers are chosen at random without replacement from $\{1,2,3, \ldots, 10\}$. The probability that minimum of the chosen number is 3 or their maximum is 7, is

If the probability that the random variable $X$ takes values $x$ is given by $P(X=x)=k(x+1) 3^{-x}$, $x=0,1,2,3, \ldots$. , where $k$ is a constant, then $P(X \geq 2)$ is equal to

A random variable $X$ takes the values 0, 1,2, 3, ..., with probability $P(X=x)=k(x+1)\left(\frac{1}{5}\right)^x$, where $k$ is $a$ constant, then $P(X=0)$ is

If $X$ follows a binomial distribution with parameters $n=8$ and $p=\frac{1}{2}$, then $p(|x-4| \leq 2)$ is equal to

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

The minimum number of times one has to toss a fair coin so that the probability of observing atleast one head is atleast 90% is

The probability of India winning a test match against West-Indies is $\frac{1}{2}$ assuming independence from match to match the probability that in a match series India’s second win occurs at the third test, is

Four dice are rolled. The probability that the same number will appear on each of them is .

Past records reveal that during a particular was, out of 9 vessels expected to arrive at the Mumbai harbour exactly 7 reached the harbour safely. If 3 vessels were expected to arrive there on a particular data, the probability that exactly two would arrive at the harbour safely, is

These are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own colour is

The probability that a marksman will hit a target is given as $1 / 5.$ Then the probablity that at least one hit in 10 shots is

If $\mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{3}{5}, \mathrm{P}(\mathrm{B} \cap \mathrm{A})=\frac{3}{10}$, then $\mathrm{P}(\mathrm{B} / \mathrm{A})$ is equal to

An unbiased coin is tossed. If the outcome is head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noticed. If the coin results in a tail then a card from a well shuffled pack of nine cards numbered $1,2,3, \ldots, 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 , is

The probability that a man will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is

If the probability of hitting a target by a shooter, in any shot, is $1 / 3$, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than $5 / 6$, is

Fifteen persons, among whom are $A$ and $B$, sit down at random at a round table. The probability that there are 4 persons between $A$ and $B$ is

Two unbiased die are rolled together.

Let $A=\{(a, b): a+b=11\}$ and $B=\{(a, b) : a \neq 5\}$, then $P(A \mid B)$ equals

The probability that a number $n$ chosen at random from 1 to 30, to satisfy $n + \left( {50/n} \right) > 27$ is

The outcome of each of 30 items was observed ; 10 items gave an outcome $\frac{1}{2} - d$ each, 10 items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$, then $\left| d \right|$ equals

Two integers are selected at random from integers 1 to 11. If the sum is even, the probability that both the numbers are odd, is

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive, is

Two cards are drawn from a pack of 52 cards. What is the probability that at least one of the cards drawn is an ace