Rolling two dice always plays a key role in probability concept. Whenever we go through the stuff probability in statistics, we will definitely have examples with rolling two dice.
Tiny dice are called dice. Large ones, like the ones a tool and die maker makes are called dies. Evelyn on August 31, 2010 1:36 pm. One mouse, two mice; one spouse two spice. I never thought about the “die is cast” thing. It’s interesting how the word dice/die just took on a new dimension for me. Thanks for sharing this.
Sample Space When 2 Dice are Rolled
- A single roll bet for 2 or 12 hi-lo-yo a single roll bet for 2, 11, or 12 high A bet on or roll of 12, also see boxcars hop A single roll bet for a specific combination of dice to come out. Pays 15:1 for easy ways and 30:1 for hard ways horn A divided bet on the 2, 3, 11, 12 horn high A horn bet with addition units going to a specific number.
- A single roll bet for 2 or 12 hi-lo-yo a single roll bet for 2, 11, or 12 high A bet on or roll of 12, also see boxcars hop A single roll bet for a specific combination of dice to come out. Pays 15:1 for easy ways and 30:1 for hard ways horn A divided bet on the 2, 3, 11, 12 horn high A.
Look at the six faced die which is given below.
The above six faced die has the numbers 1, 2, 3, 4, 5, 6 on its faces.
When a die is rolled once, the sample space is
S = {1, 2, 3, 4, 5, 6}
So, total no. of all possible outcomes = 6
When two dice are rolled,
total no. of all possible outcomes = 6 x 6 = 36
Here, the sample space is given when two dice are rolled
No downloads online games. Let us understand the sample space of rolling two dice.
For example,
(4, 3) stands for getting '4' on the first die and and '3' on the second die.
Single Dice Is Called
(1, 6) stands for getting '1' on the first die and and '6' on the second die.
Probability for Rolling 2 Dice - Formula
We can use the formula from classic definition to find probability when two dice are rolled.
or
Since there are 32 outcomes in total when two dice are rolled,
we have n(S) = 36
Practice Problems
Problem 1 :
A dice is rolled twice. What is the probability of getting a difference of 2 points?
Solution :
If an experiment results in p outcomes and if the experiment is repeated q times, then the total number of outcomes is pq.
In the present case, since a dice results in 6 outcomes and the dice is rolled twice, total no. of outcomes or elementary events is 62 or 36.
We assume that the dice is unbiased which ensures that all these 36 elementary events are equally likely.
Now a difference of 2 points in the uppermost faces of the dice thrown twice can occur in the following cases :
Thus denoting the event of getting a difference of 2 points by A, we find that the no. of outcomes favorable to A, from the above table, is 8.
By classical definition of probability, we get
P(A) = 8/36
P(A) = 2/9
Problem 2 :
Two dice are thrown simultaneously. Find the probability that the sum of points on the two dice would be 7 or more.
Solution :
If two dice are thrown then, as explained in the last problem, total no. of elementary events is 62 or 36.
Now a total of 7 or more i.e. 7 or 8 or 9 or 10 or 11 or 12 can occur only in the following combinations :
Sum = 7 -----> (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
Sum = 8 -----> (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
Sum = 9 -----> (3, 6), (4, 5), (5, 4), (6, 3)
Sum = 10 -----> ((4, 6), (5, 5), (6, 4)
Sum = 11 -----> (5, 6), (6, 5)
Sum = 12 -----> (6, 6)
Singular Dice Is Called What
Thus the no. of favorable outcomes is 21.
Letting A stand for getting a total of 7 points or more, we have
P(A) = 21/36
P(A) = 7/12
Problem 3 :
Two dice are thrown simultaneously. Find the probability of getting a doublet.
Solution :
Let us look at the sample when two dice are rolled.
In the sample space of rolling two dice, there are six cases when in which doubles are rolled. Rich man toys.
They are
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6)
Letting A stand for getting a doublet, we have
P(A) = 6/36
P(A) = 1/6
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I’ve had times when there’s been a long wait! Ugh! When you’re waiting, time seems to crawl and it is so- o-o-o boring! Have you noticed that time goes faster when you’re having fun? Well, keep dice handy for those long wait times especially when you have young children with you! It doesn’t take much room to always have a few dice in your purse or pocket just ready for appointments, airport, airplane, bus or car rides. The time seems shorter by having a little fun! I’ll share a few that I have used.
There are loads of dice game variations, but keep it simple and to their level.
Dice games are great for number recognition, patterns, and many other math skills, too!
1. Simple Dice Game:
(you can use any number of dice for this game)
Choose a number and roll the dice. You score a point every time you roll that number. When you roll that number, you get another turn. When that number is not rolled, the turn is over. Mark the tally for each time you roll the number. First one to a certain score of 10 points wins! (Set the point total low for young children and higher for older ages.)
2. Bugs
Requires only 1 die or you can speed it up by using two. With two, the player gets to choose which number they want to use for the drawing.
In this game, each number on the die represents one part of the bug.
#1 = Body, #2 =Head, #3 =Leg, #4=eye, #5= antenna, #6=tail
Each player needs to roll a #1 to start and then can add each detail to that part. For instance, you cannot add each eye until you have rolled a #2 for the head, but you can add each leg that goes on the main body (need to roll a “3” for each one) . The first player to finish their bug, wins.
You can vary this with a bunny, cat, snowman, face, mouse etc. Just decide what number stands for each part to go on the picture.
3. Pig
Requires one die
In this game each player rolls the die. If you roll anything except a “1” you can add that score or take a chance and roll again. You can keep rolling and add that number to your score until you roll a “1”. If you roll a “1 “, you lose all the amount you scored on that turn. It is the player’s option to quit at anytime and take the score up to that point. The first player to 100 wins.
4. Beat That
Each player rolls two dice and writes the highest value number that you can make with the two numbers on the dice. For instance, if a player rolls a 6 and a 1, they would write “61”. The next player rolls the dice and tries to beat that number. The player with the highest number on a round, scores a point. First player to 10 points wins. Vary this for multiplication. Multiply the two dice numbers rolled and the highest value on the round scores a point. Add a third die and then roll all three. Add the lowest two and then multiply it by the highest number. Again, the highest number of the round scores a point.
5. Going to Town
This game uses addition. Play with 3 dice. Roll and keep the highest die. Roll the remaining two and keep the highest. Roll the last die and add the three numbers for your total score. Play several rounds and the highest total wins.
6. Ladder
On a piece of paper, draw a ladder and number 1-6 on both sides of the rungs from bottom to top. This game requires two dice. Each number 1-6 is crossed off on one side before they can come back down the ladder on the other side. For instance, if a player rolls a 1 and a 2, they can cross off both the 1 and 2 or they can add them and cross off the 3. For older players, you can go to 10 on the rungs; younger players go to 6. When all the numbers are eliminated, that player wins.
There are so many variations of these games that I could go on and on. These are just a few that are handy to keep in mind when you need something to fill some time. Of course, there is Farkel and Yahtzee, but these take some strategy and are for older kids. I’m concentrating on age 4 through early elementary.
Hope these suggestions help! What are your favorite dice games? I’d love to hear your ideas.
Forgot the dice? Need a quick link to dice games online? Go to playonlinedicegames.
Playing online eliminates the interaction between parent and child along with teaching the math skills, but in a pinch it will do!
Keep those dice handy!
Have fun!
Phyllis (Oma)