Thread: Probability of Independent event

In the popular dice game Yahtzee, a Yahtzee occurs when five identical numbers turn up on a set of five standard dice. What is the probability of rolling a Yahtzee on one roll of the five dice?

This is my answer:

(1/6) ^ 5 =1/7776

However, my text has the answer as 1/1296


Where did I go wrong, or is the text wrong?

Originally Posted by john-1

In the popular dice game Yahtzee, a Yahtzee occurs when five identical numbers turn up on a set of five standard dice. What is the probability of rolling a Yahtzee on one roll of the five dice?

This is my answer:

(1/6) ^ 5 =1/7776

However, my text has the answer as 1/1296


Where did I go wrong, or is the text wrong?

There are six possible numbers for which you can get a Yahtzee so you have to multiply by 6.

multiply (1/6)^5 by six?

Originally Posted by john-1

multiply (1/6)^5 by six?

Well yes (did you do that and see you got the correct answer?).

no i didn't get the right answer, that's why i asked you if that's what you meant

$\displaystyle 6 \times \left(\frac{1}{6}\right)^5 = \frac{1}{1296}$

I just checked on my calculator

ok.. thanks, but wait, just another question.. I'm not really sure I understand how there are "six possible numbers for which you can get a Yahtzee". I understand this part
(1/6)^5 because that's like saying the identical numbers part, which means you get a yahtzee. But then when you multiply by six...how is there another six possibilities to get a yahtzee when the question says that it takes FIVE identical numbers out of six, to get a yahtzee. can you please explain.

Originally Posted by john-1

ok.. thanks, but wait, just another question.. I'm not really sure I understand how there are "six possible numbers for which you can get a Yahtzee". I understand this part
(1/6)^5 because that's like saying the identical numbers part, which means you get a yahtzee. But then when you multiply by six...how is there another six possibilities to get a yahtzee when the question says that it takes FIVE identical numbers out of six, to get a yahtzee. can you please explain.

How many numbers are there on a die? Remember you can get a yahtzee with any of the numbers. Also assuming all the dice are fair each of the numbers has an equal chance of coming up

six.. so is it something to do with the identical numbers part?

Originally Posted by john-1

six.. so is it something to do with the identical numbers part?

As Mr F said in post 2 there are 6 numbers on a fair die. As the Yahtzee can be obtained using any number (1,2,3,4,5 or 6) this means you must multiply by 6 to compensate.

If you're unsure list all the possible combinations

edit: if I rolled 5 ones I would get a yahtzee. Would I have got a Yahtzee if I'd rolled 5 fours instead? What about 5 threes