Probability (Class 12) · Question 3

JEE Advanced 2025 Paper 1MCQEasy📈 Topic in 33% papers+4−1

Three students S1, S2, and S3 are given a problem to solve. Consider the following events: U: At least one of S1, S2, and S3 can solve the problem, V: S1 can solve the problem, given that neither S2 nor S3 can solve the problem, W: S2 can solve the problem and S3 cannot solve the problem, T: S3 can solve the problem. For any event E, let P(E) denote the probability of E. If P(U) = 12, P(V) = 110, and P(W) = 112, then P(T) is equal to

1336
13
1960
14

Answer

(1) 1336

Solution

Let p1, p2, p3 be the (independent) probabilities that S1, S2, S3 solve the problem.

P(V) = p1 = 110 (independence makes the condition irrelevant).

P(U) = 1 - (1-p1)(1-p2)(1-p3) = 12 (1-p2)(1-p3) = 1/29/10 = 59.

(1-p2)(1-p3) = (1-p3) - p2(1-p3) = (1-p3) - 112.

1 - p3 = 59 + 112 = 2336 P(T) = p3 = 1336.

Answer: (A)

JEE Advanced 2025 Paper 1

Keep practising — Probability (Class 12)

A factory has a total of three manufacturing units, M1, M2, and M3, which produce bulbs independent of each other. The units M1, M2, and M3 produce bulbs in the proportions of 2:2:1, respectively. It is known that 20\% of the bulbs produced in the factory are defective. It is also known that, of all the bulbs produced by M1, 15\% are defective. Suppose that, if a randomly chosen bulb produced in the factory is found to be defective, the probability that it was produced by M2 is 25. If a bulb is chosen randomly from the bulbs produced by M3, then the probability that it is defective is .

JEE Advanced 2025 Paper 2

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 12. Also assume that the probability of the answer for a question being guessed, given that the student’s answer is correct, is 16. Then the probability that the student knows the answer of a randomly chosen question is

JEE Advanced 2024 Paper 1

Let X be a random variable, and let P(X=x) denote the probability that X takes the value x. Suppose that the points (x,P(X=x) ), x=0,1,2,3,4, lie on a fixed straight line in the xy-plane, and P(X=x)=0 for all x R-\0,1,2,3,4\. If the mean of X is 52, and the variance of X is , then the value of 24 is .

JEE Advanced 2024 Paper 1

A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For i=1,2,3, let Wi, Gi, and Bi denote the events that the ball drawn in the ith draw is a white ball, green ball, and blue ball, respectively. If the probability P(W1 G2 B3)= 25N and the conditional probability P(B3 W1 G2)= 29, then N equals .

JEE Advanced 2024 Paper 2

All Probability (Class 12) PYQs →

PDFDownload Probability (Class 12) PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Advanced Mathematics chapters

Class 11Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Conic Sections Limits and Derivatives Statistics

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)