Probability practice · Easy

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

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 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

A manufacture of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is

If $P(A)=\frac{2}{3}, P(B)=\frac{1}{2}$ and $P(A \cup B)=\frac{5}{6}$, then events $A$ and $B$ are

If $A$ and $B$ are two independent events such that $P\left( B \right) = \frac{2}{7},P\left( {A \cup {B^c}} \right) = 0.8$, then $P\left( A \right)$ is equal to

Probability of getting positive integral roots of the equation ${x^2} - n = 0$ for the integer $n,\;\,1 \le n \le 40$ is

If two dice are thrown together, then the probability that the sum of numbers appearing on them is 9, is

The probability that a student is not a car driver is $1 / 5$. The probability that out of 5 students, exactly 4 are car drivers is

An unbiased die is rolled twice. Let $A$ denote the event that an even number appears on the first throw and $B$ denote the event that an odd number appears on the second throw. Then $A$ and $B$

A letter is known to have come either from LONDON or CLIFTON; on the postmark only the two consecutive letters $\mathrm{ON}$ are legible. The probability that it came from LONDON is

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

Four numbers are multiplied together. Then the probability that the product will be divisible by 5 or 10, is

Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is

Let $A=\{1,3,5,7,9\}, B=\{2,4,6,8\}$, if a Cartesian product $A \times B$ is choosen at random, the probability of $a+b=9$ is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colours, is

Six dice are thrown simultaneously. The probability that all of them show the different faces, is