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Two numbers, X and Y, are to be chosen at random from the set of numbe

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Bunuel
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Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   07 Apr 2016, 08:35
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Two numbers, X and Y, are to be chosen at random from the set of numbers A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If it is assumed that {X = a, Y = b} is the same as the event {X = b, Y = a} for any numbers a and b in A, what is the probability that X^2 + Y^2 ≤ 27?

A. 13/90
B. 7/45
C. 17/90
D. 11/45
E. 23/90
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peachfuzz
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   07 Apr 2016, 17:11
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Two numbers, X and Y, are to be chosen at random from the set of numbers A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If it is assumed that {X = a, Y = b} is the same as the event {X = b, Y = a} for any numbers a and b in A, what is the probability that X^2 + Y^2 ≤ 27?

X^2 + Y^2 has to be ≤ 27

10! / 2!8!
there are 45 possible combinations in total

only pairs that result in a value of ≤ 27 include:
5,1
4,3
4,2
4,1
3,2
3,1
2,1

B. 7/45
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An78w
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   27 Aug 2022, 01:20
@Banuel - How do we assume here that the numbers have to be distinct?
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nidhihiremath
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   28 Aug 2022, 23:27
Hi,

Same question. Why do we not include 1,1 2,2 & 3,3 ?
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js1986
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   30 Aug 2022, 12:00
nidhihiremath wrote:
Hi,

Same question. Why do we not include 1,1 2,2 & 3,3 ?


It is like the Set consists of 9 balls numbered 1-9 and you are picking two balls. Hence you cant pick the same ball twice. I think in a set repetitions are meaningless. Correct me if wrong
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   24 Sep 2023, 17:41
Bunel please help. It is given that {X = a, Y = b} is the same as the event {X = b, Y = a} for any numbers a and b in A,. So a=b is a possibility. It is no where given that a and b are distinct. Then why we avoided pairs like (1,1)?
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   24 Sep 2023, 22:54
we can select only pairs (1,2), (1,3), (1,4), (1,5), (2,3), (2,4) and (3,4) = total 7 and if we say reverse is also true then total no of probable selections = 14

Total ways to select 2 numbers from 10 = 10*9 = 90 ways

hence probability = 14/90 = 7/45 (ans)
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   25 Sep 2023, 04:39
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Bunuel why we can’t choose same number such as (1,1) (2,2)(3,3)(4,4)?

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zahuruddin
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   25 Sep 2023, 04:46
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Because, you need to select 2 numbers from the set without keeping back the 1st number from (1 to 10), thats why pair is not possible and thats why total no of ways we can do it 10X9 = 90
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   27 Sep 2023, 07:01
pudu wrote:
Bunel please help. It is given that {X = a, Y = b} is the same as the event {X = b, Y = a} for any numbers a and b in A,. So a=b is a possibility. It is no where given that a and b are distinct. Then why we avoided pairs like (1,1)?


please someone help me to understand it...why we are not taking x=y?
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink] New post   27 Sep 2023, 07:11
zahuruddin wrote:
Because, you need to select 2 numbers from the set without keeping back the 1st number from (1 to 10), thats why pair is not possible and thats why total no of ways we can do it 10X9 = 90


but it is not given repetition is not allowed?then why we assume so?
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Re: Two numbers, X and Y, are to be chosen at random from the set of numbe [#permalink]
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