Two dice are thrown together the probability that the Event the difference of no S shown is 2 is

Probability is a part of mathematics that deals with the possibility of happening of events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event A is often written as P(A). Here P shows the possibility and A shows the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there are same chances of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event, P(A) = (Number of ways it can occur) ⁄ (Total number of outcomes)

Types of Events

• Equally Likely Events: After rolling dice, the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling.
• Complementary Events: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

What are the possible outcomes when two dice are rolled?

Answer:

A standard die has six sides numbering 1, 2, 3, 4, 5, and 6. If the die is fair, then each of these outcomes is equally likely event. Since there are six possible outcomes. The probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on.

The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6), which is 36. So, the total possible outcomes when two dice are thrown together is 36.  

The equally likely outcomes of rolling two dice are shown below:

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Similar Problems

Question 1: What are the total possible outcomes when five dice are thrown together?

Solution:

A standard die has six sides numbering 1, 2, 3, 4, 5, and 6. If the die is fair, then each of these outcomes is equally likely event. Since there are six possible outcomes, the probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on.  

The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6)multiplied by the total number of the third die(6), and so on, which is 7776. So, the total possible outcomes when three dies are thrown together is 7776.  

Question 2: What are the total possible outcomes when six dice are thrown together?

Solution:

A standard die has six sides numbering 1, 2, 3, 4, 5, and 6. If the die is fair, then each of these outcomes is equally likely event. Since there are six possible outcomes, the probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on.

The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6)multiplied by the total number of the third die(6)multiplied by the total number of the fourth die(6), and so on… which is 46656.  

So, the total possible outcomes when four dies are thrown together is 46656.

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Math Expert

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When two dice are rolled, what is the probability that the difference [#permalink]

  09 Mar 2016, 12:04

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Question Stats:

65% (01:18) correct 35% (01:25) wrong based on 172 sessions

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When two dice are rolled, what is the probability that the difference between the two numbers is 2?

(A) 1/9
(B) 2/9
(C) 1/3
(D) 2/3
(E) None of the above

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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  09 Mar 2016, 13:06

We have 8 outcomes that satisfy the question:

1-3
2-4
3-1 or 3-5
4-2 or 4-6
5-3
6-4.

For the first, second, fifth and sixth pairs the probability is (1/6*1/6)*4= 4/36. For fifth and sixth pairs probability is (1/6*2/6)*2=4/36, and the sum of all possibilities is 4/36+4/36=8/36=2/9

I think the answer is B

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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  10 Mar 2016, 20:36

Hi AlexIV,

Your work here is perfect, but it looks like you did a bunch of 'extra' math that wasn't necessary.

When you roll two 6-sided dice, there are (6)(6) = 36 possible outcomes. Once you listed the 8 options that 'fit' what the question was looking for, all you had to do was reduce the fraction:

8/36 = 2/9

Final Answer:

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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  28 Mar 2016, 04:59

I found it easiest to make a quick chart, it took about 1 min

If the top horizontal row is the first die and the first vertical row the second die then, the difference between the two is the result in the number chart.
I just counted the 2s to avoid missing any and then since it is 6x6 for all possible outcomes, then 8/36 is the answer. Hence 2/9

- 123456
1 012345
2 101234
3 210123
4 421012
5 532101
6 643210

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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  28 Mar 2016, 10:07

Hi cecammiade,

That type of 'brute force' approach is perfect for certain types of questions on Test Day. As you've pointed out, it didn't take much time or effort to do the work and THAT is something to keep in mind as you're working through the entire GMAT. Most GMAT questions can be solve in a variety of ways, so sometimes you just have to put the pen on the pad and quickly 'map out' the solution. Your willingness to think in those terms likely means that you have a high potential to score well on Test Day.

GMAT assassins aren't born, they're made,
Rich
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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  29 Mar 2016, 00:42

Bunuel wrote:

When two dice are rolled, what is the probability that the difference between the two numbers is 2?

(A) 1/9
(B) 2/9
(C) 1/3
(D) 2/3
(E) None of the above

Total Outcomes = 6*6 = 36

Favorable outcomes = {1, 3}, {2, 4}, {3, 5}, {3, 1}, {4, 6}, {4, 2}, {5, 3}, {6, 4} = 8 cases

Probability = Favorable Outcomes / Total Outcomes = 8/36 = 2/9

Answer: Option B
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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  03 May 2016, 03:23

Probability = Favorable outcomes / Total outcomes
Possible Favorable outcomes = (1,3) , (2,4) , (3,5) , (4,6) , (3,1) , (4,2) , (5,3) , (6,4)
Number of possible outcomes = 8
Total outcomes = 6 * 6 = 36

Probability = \(\frac{8}{36}\) = \(\frac{2}{9}\)
correct answer - B

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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  26 Oct 2017, 14:25

Bunuel wrote:

When two dice are rolled, what is the probability that the difference between the two numbers is 2?

(A) 1/9
(B) 2/9
(C) 1/3
(D) 2/3
(E) None of the above

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled. Of the 36 possible outcomes, there are 8 outcomes with a difference of 2: (1,3), (3,1), (2,4), (4,2), (3,5), (5,3), (4,6), (6,4). So, the probability of getting the difference of 2 is 8/36 = 2/9.

Answer: B
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Re: When two dice are rolled, what is the probability that the difference [#permalink]

  08 Oct 2022, 08:32

Given that Two dice are rolled and we need to find What is the probability that the difference between the two numbers is 2?

As we are rolling two dice => Number of cases = \(6^2\) = 36

Lets start listing down the cases where the difference between the two numbers is 2. Following are the possible cases
(1,3)
(2,4)
(3,1), (3,5)
(4,2), (4,6)
(5,3)
(6,4)

=> 8 cases

=> Probability that the difference between the two numbers is 2 = \(\frac{8}{36}\) = \(\frac{2}{9}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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Re: When two dice are rolled, what is the probability that the difference [#permalink]

08 Oct 2022, 08:32

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