When throwing 5 dice, how many times would you expect to get YATZY (5 equal) in the first throw,in 10000 times

Question

please explain what you do

Answer 1

The way to solve this problem is to consider the individual dice separately.

The first die can be any value, but each of the remaining four has to match the first, which is a 1-in-6 chance for each of the four.

So the chance of throwing a Yahtzee on a single roll is (1/6) * (1/6) * (1/6) * (1/6), which is 1/1296.

Out of 10,000 rolls, you'd expect to get 10000/1296 Yahtzees, which is 7.72. Not sure whether you'd be expected to round that off to eight.

Answer 2

The last four dice you throw have to match the first, and the probability of this happening is (1/6)^4 = 0.00077 approx. So if you try 10,000 times you would expect to get YATZY 10,000 x 0.00077 = 7.7 times, i.e. 7 or 8 times.

Answer 3

There are a total of 7776 (6*6*6*6*6) possible combinations. Of these 6 are YATZY, so the chance of YATZY is 6/7776 or
1/1296. The expected value of YATZI in 10000 throws is
10000/1296 = 7.71 or approximately 8

Answer 4

1*(1/6)*(1/6)*(1/6)*(1/6) = 1/1,296
First die can be anything (probability of 1) and the remaining dice must match the first (probability of 1/6 each).
10,000 throws
You would expect to get 5 equal dice 10,000/1,296 = 7.7 times in 10,000 throws.