Probability practice · Medium

In a lottery three were 90 tickets numbered 1 to 90. Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89, is

A sportsman's chance of shooting an animal at a distance $r > a$ ("a" is constant) is given to be $\frac{a^2}{r^2}$. He fires at $r=2 a$ and if he misses, then again fires at $r=3 a$. He repeats the same process at $r=4 a, 5 a$ and $6 a$. When he misses at $r=6 a$, the animal escapes into the jungle. If the odds against the sportsman are ${p}: {q}$, then ${q}-{p}$ is ____.

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

From a well-shuffled pack of 52 cards, four cards are selected at random. The probability of drawing exactly 2 spades and exactly 2 aces is

If $a \in \left[ { - 20,0} \right],$ then the probability that the graph of the function $y = 16\;{x^2} + 8\left( {a + 5} \right)x - 7\;a - 5$ is strictly above the $x$-axis is

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P\left(E_1\right)=\frac{2+3 p}{6}, P\left(E_2\right)=\frac{2-p}{8}$ and $P\left(E_3\right)=\frac{1-p}{2}$. If the maximum and minimum values of $p$ are $p_1$ and $p_2$, then $\left(p_1+p_2\right)$ is equal to :

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

Two non-negative integers are chosen at random. The probability that the sum of the square is divisible by 10 , is

Two dice are rolled together and the numbers $x, y$ on them form complex number $z=x+i y$. The probability that $|z| \leq 3$ is

A box contains tickets numbered 1 to 20. 3 tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 , is

If a fair coin is tossed 20 times and let we get head $n$ times, then probability that $n$ is odd, is

The probability that an event A occurs in a single trial of an experiment is 0.6 . In the first three independent trials of the experiment, the probability that A occurs atleast once is

There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7th drawn ball is 4th white, is

India plays two ODI matches each with Australia and Pakistan. The probability of India getting 0, 1, 2 are 0.45, 0.05, 0.50. The probability of India getting at least 7 points in the series is

A five-digit number (having all different digits) is formed using the digits $1,2,3,4,5,6,7,8$ and 9. The probability that the formed number either begins or ends with an odd digit, is equal to:

4 five-rupee coins, 3 two-rupee coins and 2 one-rupee coins are stacked together in a column at random. The probability that the coins of the same denominator are consecutive is

A binomial variate $\mathrm{X}$ has mean $=6$ and variance $=2$ the probability that $5 \leq \mathrm{X} \leq 7$ is

Five horses are in a race. Mr. $A$ selects two of the horses at random and bets on them. The probability that Mr. $A$ selected the winning horse, is

The random variable $X$ follows binomial distribution $B(n, p)$, for which the difference of the mean and the variance is 1 .

If $2 P(X=2)=3 P(X=1)$, then $n^{2} P(X>1)$ is equal to

Let $A$ and $B$ be two events such that $P(A)=0.3$ and $P(A \cup B)=0.8$. If $A$ and $B$ are independent events, then $P(B)=$

In order to get at least once a head with probability $\ge 0.9,$ the number of times a coin needs to be tossed is

$A$ and $B$ are two independent witnesses (ie, there is no collusion between them) in a case. The probability that $A$ will speak the truth is $x$ and the probability that $B$ will speak the truth is $y$, $A$ and $B$ agree in a certain statement. The probability that the statement is true, is

Consider the experiment of rolling a die. Let ${A}$ be the event 'getting a prime number' and $B$ be the event 'getting an odd number'.

Then, which of the following is true?

I. ${A}$ or ${B}={A} \cup {B}=\{1,2,3\}$

II. ${A}$ and ${B}={A} \cap {B}=\{3,5\}$

III. ${A}$ but not ${B}={A}-{B}=\{2\}$

IV.Not ${A}={A}^{\prime}=\{1,5,6\}$

A box conatins $2 n$ cards numbered $2^0, 2^1$, $2^2, \ldots, 2^{2 n-1}$. Two cards are taken out at random from the box, at random without replacement. Probability that sum of the numbers on the card is divisible by 3 is

A man takes a step forward with probability 0.4 and backward with probability 0.6 . The probability that at the end of eleven steps he is one step away from the starting point is

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

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

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

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