Let A be the event that the absolute differen | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the two numbers be $x$ and $y$ where $0 \le x, y \le 60$. The total area of the sample space is $60 	imes 60 = 3600$.The condition is $|x - y

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) Let the two numbers be $x$ and $y$ where $0 \le x, y \le 60$. The total area of the sample space is $60 	imes 60 = 3600$.The condition is $|x - y| \le a$,which implies $-a \le x - y \le a$.The area of the region where $|x - y| > a$ is the sum of the areas of two right-angled triangles with legs $(60 - a)$.Area of region $|x - y| > a = \frac{1}{2}(60 - a)^2 + \frac{1}{2}(60 - a)^2 = (60 - a)^2$.Thus,the area of the region where $|x - y| \le a$ is $3600 - (60 - a)^2$.Given $P(A) = \frac{3600 - (60 - a)^2}{3600} = \frac{11}{36}$.Multiplying by $3600$,we get $3600 - (60 - a)^2 = 1100$.$(60 - a)^2 = 3600 - 1100 = 2500$.$60 - a = 50 \Rightarrow a = 10$.

Let $A$ be the event that the absolute difference between two randomly chosen real numbers in the sample space $[0, 60]$ is less than or equal to $a$. If $P(A) = \frac{11}{36}$,then $a$ is equal to $...............$.

Similar Questions

$A$ card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a perfect square is

Two integers are chosen at random and multiplied. The probability that the product is an even integer is

An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

$A$ and $B$ are two events such that $P(A)=0.58$,$P(B)=0.32$ and $P(A \cap B)=0.28$. Then the probability that neither $A$ nor $B$ occurs is

Vedclass Test Series

Exam Paper Generator

Online Exam Module