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# What is the probability of rolling two fair dice and having both dice

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Math Expert
Joined: 02 Sep 2009
Posts: 46064
What is the probability of rolling two fair dice and having both dice [#permalink]

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29 Mar 2017, 04:53
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15% (low)

Question Stats:

76% (00:40) correct 24% (00:46) wrong based on 145 sessions

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What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36

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Director
Joined: 21 Mar 2016
Posts: 540
Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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29 Mar 2017, 08:45
2
odd numbers = 1,3,5

two dice will give 3 x 3 = 9 combination of odd nos... but
combination of 2 same odd nos = (1,1) (3,3) (5,5)

hence 9-3 =6

prob = 6/36 = 1/6

ans 1/6
Senior Manager
Joined: 06 Dec 2016
Posts: 251
Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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30 Mar 2017, 11:16
1
(1,3), (1,5), (3,5), (3,1), (5,1), (5,3)

6 x 6 = 36

6/36 = 1/6 which is answer C
BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 727
Location: India
GMAT 1: 710 Q49 V36
Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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30 Mar 2017, 13:00
total possible 1 3 5 (3) and 1 3 5 (3) = 9

cases excluded - 11 33 55

9-3 = 6

6/36

C
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Joined: 29 Apr 2015
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Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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30 Mar 2017, 16:49
With the regard to the popular 1/6 answer, do you guys think it is problematic that you are counting both "1,3" and "3,1" as part of your 6 positive outcomes? Does sequence matter in a dice roll?
BSchool Forum Moderator
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Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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30 Mar 2017, 22:58
ar500 wrote:
With the regard to the popular 1/6 answer, do you guys think it is problematic that you are counting both "1,3" and "3,1" as part of your 6 positive outcomes? Does sequence matter in a dice roll?

IMO , yes sequence matters

1st throw having a 1 on the dice can lead to six options on the second dice.

Assume this situation

In a Football (soccer) match , the final score is 3-1
now first player X of a team scores a hattrick , then in the dying minutes of the game , a player from the opposition scores a goal and makes it 3-1
now this score can be achieved in multiple ways and we notice that each way is different

I'm not the best person around here to explain it in a lucid way but i hope you got my point

Regards,
HK
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Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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30 Mar 2017, 23:38
The probability of one dice having odd side is 3/6=1/2. The same thing with the second dice. The probability of the second dice having distinct number is 2/3 (we have 3 possible numbers but only 2 that satisfy "distinct" condition).
Therefore general probability equals 1/2*1/2*2/3=1/6.
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Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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31 Mar 2017, 03:27
1
1
ar500 wrote:
With the regard to the popular 1/6 answer, do you guys think it is problematic that you are counting both "1,3" and "3,1" as part of your 6 positive outcomes? Does sequence matter in a dice roll?

Since the problem doesn't say that the dice are identical, think about them as two different coloured dice - one red and one yellow.
A 1 on the red die and 3 on the yellow die is different from a 3 on the red die and 1 on the yellow die.

So, there are 3 ways of getting an odd outcome on the red die and 2 ways of getting an odd outcome on the yellow die. In all there are 3*2 = 6 ways of satisfying the condition.

Of course, total cases are 6*6 = 36

Probability = 6/36 = 1/6
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Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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31 Mar 2017, 12:42
Bunuel wrote:
What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36

We need to determine the probability that the two dice show distinct odd numbers.

Let’s start with die #1: There are 3 odd numbers, and thus the probability of rolling an odd number is 3/6 = 1/2. When rolling die #2, since we must roll a different odd number, the probability of doing so is 2/6 = 1/3.

Thus, the probability is 1/2 x 1/3 = 1/6.

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What is the probability of rolling two fair dice and having both dice [#permalink]

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31 Mar 2017, 13:55
Bunuel wrote:
What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36

Solution

• Odd numbers on a die are ($$1,3$$ or $$5$$)

• We need distinct odd numbers on the two dice.

o Thus, the first die can show any one of the 3 odd numbers, which is $$= {}^3C_1$$

o The second die can then show the other 2 odd numbers, which is $$= {}^2C_1$$

o Thus, favorable cases of two dice showing distinct odd numbers $$= 3 * 2 = 6$$

• Total number of cases are $$6*6 = 36$$

• Thus, Probability $$= \frac{6}{36} = \frac{1}{6}$$

• Correct Answer is Option C.

Thanks,
Saquib
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Re: What is the probability of rolling two fair dice and having both dice [#permalink]

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03 Aug 2017, 01:35
Distinct odd values from dice 1 can have 3 outcomes.
Similarly from dice 2.
Total 6 favorable outcomes from 2 dices.
Total outcomes =36
Probability of favorable outcomes=6/36=1/6
Option C.
Re: What is the probability of rolling two fair dice and having both dice   [#permalink] 03 Aug 2017, 01:35
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