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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?

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

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.

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.

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.

Answer: C
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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.

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