New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Probability question

2024 · 30 Jan · Shift 1 · Q43

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Mathematics
Probability
2024 · 30 Jan · Shift 1 · Q43

Probability question

2024 · 30 Jan · Shift 1 · Q43

JEE MainMathematicsProbabilityMCQ+4 / −1

Two integers

x

and

y

are chosen with replacement from the set

\{0,1,2,3, \ldots, 10\}

. Then the probability that

|x-y|\gt 5

, is :

A
$\frac{31}{121}$
B
$\frac{60}{121}$
C
$\frac{62}{121}$
D
$\frac{30}{121}$

View written solutionFree

Correct answer: D

Total number of outcomes

Since $x$ and $y$ are chosen with replacement from the set

\{0,1,2,3,\dots,10\}

there are $11$ choices for $x$ and $11$ choices for $y$ .

So total ordered pairs:

11\times 11=121

Required condition

We need:

|x-y|>5

This means:

|x-y|=6,7,8,9,10

Count favorable pairs

For a fixed difference $d>0$ , the number of ordered pairs satisfying $|x-y|=d$ is:

2(11-d)

because:

$x-y=d$ gives $11-d$ pairs,
$y-x=d$ gives another $11-d$ pairs.

Now compute for $d=6,7,8,9,10$ :

For $d=6$ :

2(11-6)=2\cdot 5=10

For $d=7$ :

2(11-7)=2\cdot 4=8

For $d=8$ :

2(11-8)=2\cdot 3=6

For $d=9$ :

2(11-9)=2\cdot 2=4

For $d=10$ :

2(11-10)=2\cdot 1=2

Total favorable outcomes:

10+8+6+4+2=30

Probability

Therefore,

P(|x-y|>5)=\frac{30}{121}

Option matching

\frac{30}{121}

corresponds to Option D.

Comparison with stored answer

Stored correct answer: D

This matches our derived answer.

More from Probability

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics,…2024 · Numerical
Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is2024 · MCQ
Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $x$ to be the number of rotten apples in a draw of two apples, the variance of $x$ is2024 · MCQ
Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is…2024 · MCQ
A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is2024 · MCQ
Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{st}$ die is less than the number appeared on the $2^{nd}$ die, $B$ be the event that the number appeared on the…2023 · MCQ
Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$ , where $p$ and $q$ are co-prime, then $q - p$ is equal to :2023 · MCQ
In a bolt factory, machines $C$ and $C$ manufacture respectively $50%$ and $50%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt…2023 · MCQ