Probability

JEE Main 2025 (Online) 28th January Morning ShiftMCQEasy📈 Topic in 37% papers+4−1

Ques. 1JEE Main 2025, 28 January (Morning Shift)

Two numbers k1 and k2 are randomly chosen from the set of natural numbers. Then, the probability that the value of ik1 + ik2, (i = -1) is non-zero, equals

Answer

(1) 34

Solution

ik depends only on the remainder of k on division by 4, and the four remainders are equally likely.

So (ik1, ik2) has 4 4 = 16 equally likely cases, each of ik1, ik2 \i, -1, -i, 1\.

ik1 + ik2 = 0 ik2 = -ik1: for each value of ik1 exactly one value of ik2 works 4 cases.

P(sum = 0) = 416 = 14

P(sum non-zero) = 1 - 14 = 34

Answer: (1)

Keep practising — Probability

Ques. 2JEE Main 2025, 28 January (Evening Shift)

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

Ques. 3JEE Main 2025, 23 January (Morning Shift)

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

Ques. 4JEE Main 2025, 23 January (Evening Shift)

A board has 16 squares as shown in the figure : [figure] Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

35
45
2330
710

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All JEE Main Mathematics chapters

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