Can someone figure out this math/probability question??

[Mighty Favog]

Lorrie and I were rolling dice to see who gets the first roll/turn at a game of Yahtzee. We each rolled a single die and it came up with the same number 4X before we could start playing.

 

Now what's the chance of that happening??

[Edgar]

4 minutes ago, Mighty Favog said:

Lorrie and I were rolling dice to see who gets the first roll/turn at a game of Yahtzee. We each rolled a single die and it came up with the same number 4X before we could start playing.

 

Now what's the chance of that happening??

 

There is a 1/6 probability of any selected number coming up on any roll. If it's a fair die, then each roll is independent of the others. So the probability is (1/6)^4 = 1/1296.

 

If it's a loaded die, then the probability is greater than that.

[PrestonTom]

Noticed that Edgar said "selected number".

 

So, yes the calculation is correct (if you said before the 1st roll) the probability of a "four", but you could have said (before any roll) any of the 5 other numbers. So the probability is a higher, ( that 4 rolls would be the same number, but not necessarily a specific number) but overall it is still quite small. 

[Edgar]

4 minutes ago, PrestonTom said:

Noticed that Edgar said "selected number".

 

So, yes the calculation is correct (if you said before the 1st roll) the probability of a "four", but you could have said (before any roll) any of the 5 other numbers. So the probability is a higher, ( that 4 rolls would be the same number, but not necessarily a specific number) but overall it is still quite small. 

 

That's a really good point that I missed. If you select the target number before any rolls, then the probability is as I indicated above. But if you count as a success any number coming up four times in a row, then the probability is increased 6x because there are six numbers. That is to say, "1,1,1,1" is a success, as is "2,2,2,2", "3,3,3,3", etc.

[Gilbert]

Equation is way off. There were 2 dice being rolled, for which equal back to back results occurred 4 times.

 

Enter theories of probability and statistics

[Mighty Favog]

If this makes any difference, it went something like: first roll = 4 on both dice, second roll = 1 on both dice, third roll on = 6 on both dice, fourth roll = 2 on both dice.

[Edgar]

14 minutes ago, Mighty Favog said:

If this makes any difference, it went something like: first roll = 4 on both dice, second roll = 1 on both dice, third roll on = 6 on both dice, fourth roll = 1 on both dice.

Yes, entirely different problem. I misunderstood.

 

EDIT: But I think that the answer comes up the same, depending upon how you state it.

 

First roll: You roll a 4, what is the probability that your wife will roll a 4? 1/6

Second roll: You roll a 1, what is the probability that your wife will roll a 1? 1/6

Third roll: You roll a 6, what is the probability that your wife will roll a 6? 1/6

Fourth roll: You roll a 1, what is the probability that your wife will roll a 1? 1/6

Total probability: (1/6)^4

 

Looked at it another way ...

First roll: What is the probability that you will both roll a 4? 1/6 * 1/6

Second roll: What is the probability that you will both roll a 1? 1/6 * 1/6

Third roll: What is the probability that you will both roll a 6? 1/6 * 1/6

Fourth roll: What is the probability that you will both roll a 1? 1/6 * 1/6

Total probability: (1/36)^4

 

And yet another way ...

First roll: What is the probability that you will both roll the same number? 6 * 1/6 * 1/6 = 1/6

Second roll: What is the probability that you will both roll the same number? 6 * 1/6 * 1/6 = 1/6

Third roll: What is the probability that you will both roll the same number? 6 * 1/6 * 1/6 = 1/6

Fourth roll: What is the probability that you will both roll the same number? 6 * 1/6 * 1/6 = 1/6

Total probability: (1/6)^4

 

Computing probabilities always gave me fits.

Edited August 4, 2022 by Edgar
Elaboration

[KobeWinters]

I know math is a challenging subject. And probability is one of the most ""painful"" module. However, if I understood it, you can do it too. Be patient with yourself. Don't get discouraged if you don't understand something immediately. Keep practicing and you will improve. The worksheets from https://www.worksheetsgo.com may be helpful. Besides, don't hesitate to seek help from a teacher, tutor, or peer. I used to relate mathematical concepts to real-life situations or other subjects I was familiar with. You can do it too and see if it works. Hope I helped!

Edited February 3 by KobeWinters

[Travis In Austin]

It is 6 to the negative 4 power

 

5 times the same number on each die is 6 to the negative 5 power

 

To roll that same sequence of numbers again is 6 to the negative 8 power, starting to get into lottery odds

[Travis In Austin]

What are the odds of getting out of jail by rolling doubles (rolling doubles 1x on 3 attempts)

[artto]

Just curious. What did you use to "roll" the dice?

 

Was it your hands? Or was it a cup or something like they use at a Casino?

 

There's a reason they don't let you "roll" the dice from your hand. Some people (like myself) apparently hold or throw the dice a certain way (this can be a very natural thing - unpracticed). I am one of those people.

 

A long time ago my best friend said I couldn't roll doubles more than 2x in a row. I promptly proved him wrong, and did it way more then 2x. Also, I seem to have a knack for doing the same thing with my heart meds. When taking them out of the container and "drop" them on the counter very frequently they land/stand on edge. Kind of pisses me off actually. Because then they tend to roll away & I have to catch them before they hit the floor so my dog doesn't get them. OTOH, IF I deliberately tried to drop them on edge it seems to never work. LOL Go figure.

[Mighty Favog]

13 minutes ago, artto said:

Just curious. What did you use to "roll" the dice?

 

Was it your hands? Or was it a cup or something like they use at a Casino?

 

There's a reason they don't let you "roll" the dice from your hand. Some people (like myself) apparently hold or throw the dice a certain way (this can be a very natural thing - unpracticed). I am one of those people.

 

A long time ago my best friend said I couldn't roll doubles more than 2x in a row. I promptly proved him wrong, and did it way more then 2x. Also, I seem to have a knack for doing the same thing with my heart meds. When taking them out of the container and "drop" them on the counter very frequently they land/stand on edge. Kind of pisses me off actually. Because then they tend to roll away & I have to catch them before they hit the floor so my dog doesn't get them. OTOH, IF I deliberately tried to drop them on edge it seems to never work. LOL Go figure.

It was our hands.

[dirtmudd]

https://www.thoughtco.com/probability-of-rolling-a-yahtzee-3126593