class 12

Math

Algebra

Probability I

If two different numbers are taken from the set ${0,1,2,3,……,10};$then the probability that their sum as well absolute difference are both multiple of $4,$is:

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Two integers x and y are chosen with replacement out of the set {0, 1, 2, 3, …, 10}. Then find the probability that $∣x−y∣>5$.

Three faces of a fair dice are yellow, two are red and one is blue. Find the probability that the dice shows (a) yellow, (b) red and (c ) blue face.

If out of 20 consecutive whole numbers two are chosen at random, then find the probability that their sum is odd.

A sample space consists of 3 sample points with associated probabilities given as $2p,p_{2},4p−1$. Then the value of p is

There are two die A and B both having six faces. Die A has three faces marked with 1, two faces marked with 2, and one face marked with 1, two faces marked with 2, and one face marked with 3. Die B has one face marked with 1, two faces marked with 2, and three faces marked with 3. Both dices are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and let P(E) be the probability of event E, then P(E) is maximum when x equal to

A bag contains 3 red, 7 white, and 4 black balls. If three balls are drawn from the bag, then find the probability that all of them are of the same color.

2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is

In a certain city, only 2 newspapers A and B are published. It is known that 25% of the city population read A and 20% read B while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisement and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. What is the percentage of the population who read an advertisement?