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Test on Probability

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Question 1

If the integers m and n are chosen at random from 1 and 100, then the probability that a number of from 7^m + 7ⁿ is divisible by 5, equals

Question 2

In a certain test, there are n questions. In this test, 2^k students gave wrong answers to at least (n – k) questions, where k = 0, 1, 2, ….. n. If the total number of wrong answer is 4095, then the value of n is

Question 3

If x = 33ⁿ, n is a positive integral value, then what is the probability that x will have 3 at its units place, when n is selected at random

Question 4

A coin is tossed 2n times, then probability of getting one head more in the last n tosses as in the first n tosses is

Question 5

A letter is supposed to have come either from “LONDON” or from “CLIFTON”. On the postmark only two consecutive letters “ON” are visible. The chance that it has come from “LONDON” will be

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Dec 3JEE & BITSAT