Probability of Dice

Learn about dice probability. How do you calculate the probability of rolling an 8 with a pair of dice?
You can calculate the probability of rolling a number by using the number of favorable events divided by the number of total events.

[tofxdod]

That's a very good explanation!
Many people also get the following question wrong, so please explain.
[Question]
Find the probabilities that the following events will occur when two dice are rolled.
①Both show odd numbers
②One shows odd number and another shows evenn number
③Both show even number

P(E):the probability that event E occurs.

【Distinguishable dice A and B】
(the number that dice A shows, the number dice B shows):event
If we only judge whether the numbers indicated by the dice are odd or even, the following four events will occur.
　　(odd, odd) (odd, even)

　　(even, odd) (even, even)
If each event occurs with equal probability, the probability is 1/4.
Therefore, P(①)=1/4, P(②)=1/2, P(③)=1/4 (1)
If we judge the number(1, 2, ···, 6) indicated by the dice, the following 36 events will occur.
(1, 1), (1, 3), (1, 5) (1, 2), (1, 4), (1, 6)
(3, 1), (3, 3), (3, 5) (3, 2), (3, 4), (3, 6)
(5, 1), (5, 3), (5, 5) (5, 2), (5, 4), (5, 6)

(2, 1), (2, 3), (2, 5) (2, 2), (2, 4), (2, 6)
(4, 1), (4, 3), (4, 5) (4, 2), (4, 4), (4, 6)
(6, 1), (6, 3), (6, 5) (6, 2), (6, 4), (6, 6)
If each event occurs with equal probability, the probability is 1/36.
Therfore
P(①)=9×(1/36)=1/4, P(②)=18×(1/36)=1/2, P(③)=9×(1/36)=1/4 (2)
(2) matches (1).

【Indistinguishable two dice】
(odd, even)is the same event as(even, odd).
Thererore, if we only judge whether the numbers indicated by the dice are odd or even, the following three events will occur.
　　(odd, odd)

　　(even, odd) (even, even)
If each event occurs with equal probability, the probability is 1/3.
Therefore
P(①)=1/3, P(②)=1/3, P(③)=1/3 (3)
(1, 3) is the same event as (3, 1).
If we judge the number(1, 2, ···, 6) indicated by the dice, the following 21 events will occur.
(1, 1)
(3, 1), (3, 3)
(5, 1), (5, 3), (5, 5)

(2, 1), (2, 3), (2, 5) (2, 2)
(4, 1), (4, 3), (4, 5) (4, 2), (4, 4)
(6, 1), (6, 3), (6, 5) (6, 2), (6, 4), (6, 6)
If each event occurs with equal probability, the probability is 1/21.
Therefore
P(①)=6×(1/21)=2/7, P(②)=9×(1/21)=3/7, P(③)=6×(1/21)=2/7 (4)
(4) contradicts (3).

[darklewd]

Thank you. Now I can't lose my dice roll while playing Yugioh anymore.

[Vivldi]

Best explenation ever, my math teacher never mentioned this stuff

[edgardocodillo]

A 10 sided die is tossed. What is the probability of getting:

a. multiple of 3

b. divisors of 8

c. numbers less than 10

d. cube numbers

e. square numbers

[dominiquesanders]

Hello need help with this one --
Show logical notation that expresses following statement: If one dice shows an even number of spots and the second dice shows an odd number of spots, then the total for the pair is less than or equal to 9.

[Vivldi]

whats the difference between probability and odds? In my language it means both the same :(

[PostGodz]

What if the question says rolling a special number?

[TheMitchellWhite]

I think you were meant to say “2 and 12.” Not 1. There is no chance of one haha

[imrandom]

K.I.S.S thats for everyone. This shit aint complicated

[LrCloud]

If you roll two dice the chances of you
rolling a double is 1/6
rolling a chosen double (5 and 5 for example) is 1/36

...I make the proposition that making a guess of a number between 1 and 6 is like rolling a dice in your head.
So, if you throw a dice 1/6
And guess the number the probability of you guessing correctly the same as throwing two dice?

...so shouldn't the chance of you guessing correctly be 1/36....?
(Yet you and I both know that rolling a dice can only yield 6 possible outcomes)

So is the probability 1/6 or 1/36....?