Class 12

Math

Algebra

Probability I

Two dice are rolled once. Find the probability of getting such numbers on two dice whose product is perfect square.

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If A and B are two events, the probability that exactly one of them occurs is given by

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.

A five-digit number is formed by the digit 1, 2, 3, 4, 5 without repetition. Find the probability that the number formed is divisible by 4.

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

Three houses are available in locality. Three persons apply for the houses. Each applies for one houses without consulting others. The probability that all three apply for the same houses is

A bag contains b blue balls and r red balls. If two balls are drawn at random, the probability drawing two red balls is five times the probability of drawing two blue balls. Furthermore, the probability of drawing one ball of each color is six times the probability of drawing two blue balls. Then

If the squares of a $8×8$ chessboard are painted either red or black at random. The probability that not all the squares in any column are alternating in color is

Let A = {0, 5, 10, 15, …, 195}. Let B be any subset of A with at least 15 elements. What is the probability that B has at least one pair of elements whose sum is divisible by 15?