• Support PF! Buy your school textbooks, materials and every day products Here!

Probability of two ones with 6 dice

  • #1
104
0

Homework Statement



What is the probability of rolling exactly two ones from a set of six dice?

Homework Equations


Binomial probability distribution?


The Attempt at a Solution


I tried:

P = 6!/(2! x 4!) x (1/6)^2 x (5/6)^4 and got 0.20, but the book says that's a factor of 10 too high!
 

Answers and Replies

  • #2
286
0
relevant equation is correct... but, let's look at it this way:

You could get a 1,1,something else, something else, something else, something else.
Probability is 1/6 * 1/6 * 5/6 * 5/6 * 5/6 * 5/6
Or, you could get a
something else, 1, something else, something else, 1, something else
Probability is 5/6 * 1/6 * 5/6 * 5/6 * 1/6 * 5/6

Note, the probabilities of these two are the same; after a bit of rearranging,
(1/6)^2 * (5/6)^4

Now, how many different orders can you get 2 ones and 4 something elses?
The ones can be 1st and 2nd, 1st and 3rd, 1st and 4th, 1st and 5th, or 1st and 6th. Or, 2nd and 3rd, 2nd and 4th, etc. This is a combination of 2 elements out of 6, sometimes written as 6C2. (I don't know which way you've learned to write it.)

So, put these two parts together, and you should get your answer.
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618
Whoever figured out the answers in your book is high on something. Your answer is correct.
 

Related Threads on Probability of two ones with 6 dice

  • Last Post
Replies
22
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
4
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
13K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
504
  • Last Post
Replies
2
Views
4K
Replies
3
Views
737
  • Last Post
Replies
13
Views
5K
Top