Question

We toss two dice 1,000 times. How many times do we expect to have the sum of the two dice equal to 4?


about 250

about 167

about 83

about 42

Answer 1

Let's first look at how many combinations we can make w/two die to get four:
1 + 3
3 + 1
2 + 2
Right?
So, 3 ways to make 4 with 2 die.
Now, How many possible combinations can we get with 2 die?
Well, there are 6 sides, and 6 possible sides to pair with:
6 x 6 = 36
So we have a 3/36 chance of rolling 4, simplify that to 1/12
Now, let's make a proportion:
1/12 = x/1000
This means that if we have a 1/12 chance of rolling 4, it should be proportional to something over 1000
Cross-multiply:
1000=12x
Divide:
x = 83. 33333 ...
So about 83 times