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What is the probability of getting a number on the first throw greater

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What is the probability of getting a number on the first throw greater [#permalink]

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New post 16 Feb 2017, 17:42
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What is the probability of getting a number on the first throw greater than that on the second throw when a dice is thrown twice?

A. 1/6
B. 2/3
C. 5/12
D. 7/12
E. 5/6
[Reveal] Spoiler: OA
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Re: What is the probability of getting a number on the first throw greater [#permalink]

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New post 16 Feb 2017, 18:47
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ssr300 wrote:
What is the probability of getting a number on the first throw greater than that on the second throw when a dice is thrown twice?

A. 1/6
B. 2/3
C. 5/12
D. 7/12
E. 5/6



Hi,

1) simple logic should tell us that answer should be near but LESS than 1/2..
As we are dealing with duplicate patterns.. 1 and 6..... 2 and 5...3 and 4...
C should be the guess..
Why it should be near half is in the method below.

2) there can be six numbers in first throw and six in second , so ways = 6*6*=36..

Now if 1 is in first throw, any number in 2nd throw except 1 itself will give you ans YES, so 5 throw..
But in 2, all except 1 and itself will bE so 6-2=4 ways..
Similarly 3,2,1 and 0 for number 4,3,2,and 1respectively in first throw..
Possible ways=5+4+3+2+1+0=15..

Prob =15/36=5/12..
C
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Re: What is the probability of getting a number on the first throw greater [#permalink]

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New post 16 Feb 2017, 21:01
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A= number on first throw
B= number on 2nd throw

There are 3 options here.
A=B, A<B, A>B.

The probability of A=B is 1/6.
So the probability of A<B and A>B is 5/6.
1/2 of which be greater and 1/2 will be lower.
So 1*5/2*6 =5/12 is the probability for A>B.
Ans C.

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Re: What is the probability of getting a number on the first throw greater [#permalink]

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New post 17 Feb 2017, 12:06
chetan2u wrote:
ssr300 wrote:
What is the probability of getting a number on the first throw greater than that on the second throw when a dice is thrown twice?

A. 1/6
B. 2/3
C. 5/12
D. 7/12
E. 5/6



Hi,

1) simple logic should tell us that answer should be near but LESS than 1/2..
As we are dealing with duplicate patterns.. 1 and 6..... 2 and 5...3 and 4...
C should be the guess..
Why it should be near half is in the method below.

2) there can be six numbers in first throw and six in second , so ways = 6*6*=36..

Now if 1 is in first throw, any number in 2nd throw except 1 itself will give you ans YES, so 5 throw..
But in 2, all except 1 and itself will bE so 6-2=4 ways..
Similarly 3,2,1 and 0 for number 4,3,2,and 1respectively in first throw..
Possible ways=5+4+3+2+1+0=15..

Prob =15/36=5/12..
C


exactly my approach...yet I used approximations.
the odds should be slightly less than 1/2
A is too little
B is too big
C is close
D is too big
E is too big.

C remains
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Re: What is the probability of getting a number on the first throw greater [#permalink]

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New post 17 Feb 2017, 23:30
if in first through prob of getting 1 is 1/6 but in this case other number greater than 1 will be 5/6
similarly prob of getting 2 is 1/6 but in this case other number greater than 2 will be 4/6

adding till 5
1/6( 5/6+ 4/6....1/6)= 5/12

C is the answer
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Re: What is the probability of getting a number on the first throw greater [#permalink]

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New post 18 Feb 2017, 03:05
Probability of getting it is 1/2 minus the probability of getting the same number on both throws which is 1/12.

(1/2) - (1/12) = 5/12

Option C
Re: What is the probability of getting a number on the first throw greater   [#permalink] 18 Feb 2017, 03:05
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