Class 12

Math

Algebra

Probability I

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of number of jacks.

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A bag contains 50 tickets numbered 1, 2, 3, …, 50 of which five are drawn at random and arranged in ascending order of magnitude $(x_{1}<x_{2}<x_{3}<x_{4}<x_{5})$. Find the probability that $x_{3}=30$.

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.

A fair coin is tossed 5 times. Find the probability that no two consecutive heads occur.

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

South African cricket captain lost the toss of a coin 13 times out of 14. The chance of this happening was

Four candidates A, B, C and D have applied for the post in government office. If A is twice as likely to be selected as B, and B and C are given about the same chances of being selected, while C is twice as likely to be selected as D, what are the probabilities that (i) C will be selected? (ii) A will not be selected?

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

The number 1, 2, 3, …, n are arrange in a random order. The probability that the digits 1, 2, 3,…, $k(k<n)$ appear as neighbors in that order is