This one is a challenge: What is the probability of drawing a “double” from a set of dominoes?

Question

In a set of dominos, each tile has two sides with a number of dots on each side: zero, one, two, three, four, five or six. There are 28 total tiles, with each number of dots appearing alongside each other number (including itself) on a single tile.

Question 1: What is the probability of drawing a “double” from a set of dominoes — that is, a tile with the same number on both sides?

Question 2: Now you pick a random tile from the set and uncover only one side, revealing that it has six dots. What’s the probability that this tile is a double, with six on both sides?

Answer 1

Answer 2

Hi Nadia C.,

a) There are only single tiles which present: 0/0, 1/1, 2/2, 3/3, 4/4, 5/5, and 6/6 . So that's 7 tiles out of 28, P = 1/4.

b) a tile with a 6 on one side could have any of 0, 1, 2, 3, 4, 5, or 6 on the other side. So that's P = (1/7) .

Hint: on problems such as this, especially if you aren't familiar with dominos, it might help to just jot down the possibilities: 0/0, 0/1, 0/2 .... 6/6, so that you can see that there are 28 possibilities (7+6+5+4+3+2+1) . Otherwise, you might visualize a 7x7 choice array, which would steer you in totally the wrong direction!

-- Cheers, -- Mr. d.

Answer 3

Another explanation of my answer to question 2: There are seven dominoes with a six dot side - six singles and one double. That makes a total of 8 sides with six dots. Two of them are on the double. 2/8 = .25

Answer 4

1 - 7 of the 28 dominoes are doubles, so p = .25

2 - this is a tough one. My intuition tells me that the fact that the random tile has six dots on one side does not change the answer and p is still .25

Answer 5

Note the difference between dice and dominoes: In dice, you can have a 1 and 6 or a 6 and 1, while in dominoes, you only have a domino with a 1 and 6.

Thus, there are 7 dominoes that are doubles: (0, 0), (1, 1), ... (6, 6) and 28 dominoes total, so the chance of drawing a double is 7/28 = 1/4 (with dice, the chance of a double is 6/36 = 1/6)

The answer may surprise, but it is 2/8 = 1/4. That is because there are 8 sides that have 6 dots (2 on the (6,6) and 1 each on the (0, 6), (1, 6), ..., (5,6)), and on 2 of the 8 (either side of the double 6), there is a 6 on the other side.