Probability

JEE Main 2025 (Online) 4th April Morning ShiftMCQMedium📈 Topic in 37% papers+4−1

Ques. 1JEE Main 2025, 4 April (Morning Shift)

The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

129182
1726
1926
103182

Answer

(1) 129182

Solution

Total persons = 16 ⇒ n(S) = 16C12 = 16C4 = 1820

Favourable cases (engineers E, doctors D, professors P):

E = 3, D = 1, P = 8: 4C3 2C1 10C8 = 4 2 45 = 360

E = 3, D = 2, P = 7: 4C3 2C2 10C7 = 4 1 120 = 480

E = 4, D = 1, P = 7: 4C4 2C1 10C7 = 1 2 120 = 240

E = 4, D = 2, P = 6: 4C4 2C2 10C6 = 1 1 210 = 210

⇒ n(E) = 360 + 480 + 240 + 210 = 1290

∴ P = 12901820 = 129182

Answer: (1)

Keep practising — Probability

Ques. 2JEE Main 2025, 2 April (Morning Shift)

Three distinct numbers are selected randomly from the set \1, 2, 3, , 40\. If the probability, that the selected numbers are in an increasing G.P., is mn, (m, n) = 1, then m + n is equal to .

Ques. 3JEE 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

Ques. 4JEE 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. 5JEE 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. 6JEE 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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