Part 2 ยท Two Dice
๐ŸŽฏ INTERACTIVE

Two dice: what is the probability of a sum of 7?

Total combinations: 6 ร— 6 = 36. How many give a sum of 7?

๐ŸŽฒ1
๐ŸŽฒ2
๐ŸŽฒ3
๐ŸŽฒ4
๐ŸŽฒ5
๐ŸŽฒ6
๐ŸŽฒ1
2
3
4
5
6
7
๐ŸŽฒ2
3
4
5
6
7
8
๐ŸŽฒ3
4
5
6
7
8
9
๐ŸŽฒ4
5
6
7
8
9
10
๐ŸŽฒ5
6
7
8
9
10
11
๐ŸŽฒ6
7
8
9
10
11
12
Press โ†“ to highlight combinations that sum to 7 6 combinations give a sum of 7: (1,6) (2,5) (3,4) (4,3) (5,2) (6,1)

P(sum = 7) = 6/36 = 1/6 ~ 16.7%

Seven is the most common sum. But two (1+1) is only 1/36 ~ 2.8%

Part 2 ยท Two Dice

Not all sums are equally likely

Sum Combinations Probability
2 1 2.8%
3 2 5.6%
4 3 8.3%
5 4 11.1%
6 5 13.9%
7 6 16.7%
8 5 13.9%
9 4 11.1%
10 3 8.3%
11 2 5.6%
12 1 2.8%

Not all outcomes are equally likely, even if they feel like they should be.
That misunderstanding is exactly what makes casinos money.