New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Probability question

2025 · Shift 1 · Q18

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Probability
2025 · Shift 1 · Q18

Probability question

2025 · Shift 1 · Q18

JEE AdvancedMathematicsProbabilityMCQ+3 / −1

Three students

S_1, S_2,

and

S_3

are given a problem to solve. Consider the following events: U: At least one of

S_1, S_2,

and

S_3

can solve the problem, V:

S_1

can solve the problem, given that neither

S_2

nor

S_3

can solve the problem, W:

S_2

can solve the problem and

S_3

cannot solve the problem, T:

S_3

can solve the problem. For any event

E

, let

P(E)

denote the probability of

E

. If

P(U) = \dfrac{1}{2}

,

P(V) = \dfrac{1}{10}

, and

P(W) = \dfrac{1}{12}

, then

P(T)

is equal to

A
$\dfrac{13}{36}$
B
$\dfrac{1}{3}$
C
$\dfrac{19}{60}$
D
$\dfrac{1}{4}$

More from Probability

A factory has a total of three manufacturing units, $M_{1}, M_{2}$ , and $M_{3}$ , which produce bulbs independent of each other. The units $M_{1}, M_{2}$ , and $M_{3}$ produce bulbs in the proportions of $2 : 2 : 1$ , respectively. It is known that $20%$ …2025 · Numerical
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…2024 · MCQ
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 $x y$ -plane, and $P (X = x) = 0$ for all $x \in R - {0, 1, 2, 3, 4}$ …2024 · Numerical
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 $i = 1, 2, 3$ …2024 · Numerical
Let $X = {(x, y) \in Z \times Z : \frac{x ^{2}}{8} + \frac{y ^{2}}{20} < 1$ and $y^{2} < 5 x}$ . Three distinct points $P, Q$ and $R$ are randomly chosen from $X$ . Then the probability that $P, Q$ and $R$ …2023 · MCQ
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$ , then the probability that the experiment stops with head is :2023 · MCQ
Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44422 are not in $X$ . Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional…2023 · Numerical
Consider the $6 \times 6$ square in the figure. Let $A_{1}, A_{2}, \dots, A_{49}$ be the points of intersections (dots in the picture) in some order. We say that $A_{i}$ and $A_{j}$ are friends if they are adjacent along a row or along a column.… Includes diagram2023 · Numerical