Probability practice · Mixed difficulty

There is a five-volume dictionary among 50 books arranged on a shelf in a random order. If the volumes are not necessarily kept side-by side, the probability that they occur in increasing order from left to right is

The chances of defective screws in three boxes A, B, C are $\frac{1}{5}, \frac{1}{6}, \frac{1}{7}$ respectively. A box is selected at random and a screw drawn from it at random is found to be defective. Then the probability that it came from box $A$ is

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to the probability of getting 9 heads, then the probability of getting 2 heads is

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

If the independent events $A$ and $B$ are such that $0 < P(A) < 1$ and $0 < P(B) < 1$, then which of the following alternatives is not correct?

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

In a class $60 \%$ passed their Physics examination and $58 \%$ passed in Mathematics. Atleast what percentage of students passed both their Physics and Mathematics examination?

In a binomial distribution, mean is 3 and standard deviation is $\frac{3}{2}$, then the probability distribution is

If ten objects are distributed at random among ten persons, the probability that at least one of them will not get any thing is

$A$ box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white balls, 4 red balls and 5 black balls. If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box $B_2$ is

A number $n$ is chosen at random from {1, 2, 3, 4, ……….,1000}. The probability that $n$ is a number that leaves remainder 1 when divided by 7, is

In a market research project, $20 \%$ opted for 'Nirma' detergent whereas $60 \%$ opted for 'Surf blue' detergent. The remaining individuals were not certain. If the difference between those who opted for 'Surf blue' and those who were uncertain was 720 , how many respondents were covered in the survey

A natural number is selected from 1 to 1000 at random, then the probability that a particular non-zero digit appears at most once, is

Four fair dice are thrown simultaneously. If the probability that the highest number obtained is 4 is $\frac{25 a}{1296}$ then &#39; $a$ &#39; is equal to

A fair coin is tossed repeatedly. The probability of getting a result in fifth toss different from those obtained in the first four tosses 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

Box $A$ contains 2 black and 3 red balls. While box $B$ contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing box $A$ is double that of box $B$. If a red ball is drawn from the selected box, then the probability that it has come from box $B$. 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

One ticket is selected at random from 100 tickets numbered $00,01,02, \ldots, 99$.
Suppose, $X$ and $Y$ are the sum and product of the digit found on the ticket $P(X=7 / Y=0)$ is given by

Two unbiased dice are thrown simultaneously. The probability to get a sum more than 8 is

Let the sum of two positive integers be 24. If the probability, that their product is not less than $\frac{3}{4}$ times their greatest positive product, is $\frac{\mathrm{m}}{\mathrm{n}}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{n}-\mathrm{m}$ equals:

Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is

Numbers 1,2,3,..., 100 are written down on each of the cards A, B and C. One number is selected at random from each of the cards. The probability that the numbers so selected can be the measures (in cm) of three sides of a right-angled triangle 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

A pair of fair dice is thrown independently 4 times. The probability of getting a sum of exactly 7 twice 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

If the events $A$ and $B$ are independent, then $P(A \cap B)$ is equal to

Let $A$ and $B$ be two events such that $P(A)$ $=3 / 7, P(B)=4 / 7$ and $P(A \cup B)=5 / 7$,
then $\frac{P(A \mid B)}{P\left(A^{\prime} \mid B\right)}$ equals

If $P\left( A \right) = \frac{1}{{12}},\;P\left( B \right) = \frac{5}{{12}}$ and $P\left( {\frac{B}{A}} \right) = \frac{1}{{15}},$ then $P\left( {A \cup B} \right)$ is equal to