If you roll a PAIR of dice, what is P(<7, 2 dice)? Give your answer in decimal form.

Question

Now that you have drawn the dice table, find the probability. These problems use some abbreviations: P(4, 2 dice) means what is the probability of getting a 4 when you roll two dice. 

Answer 1

Hm, I assume P(<7, 2 dice) is "the probability of getting two numbers that add up to less than 7, when you roll two dice".

If you're rolling two dice, your sample space is (1, 2, 3, 4, 5, 6) x (1, 2, 3, 4, 5, 6). It has a size of 36. In other words, there are 36 different combinations of ordered pairs you can generate by rolling two dice.

Now we count the number of cases where the two numbers of this ordered pair add up to less than 7.

First dice is 1: (1, 1) (1, 2) (1, 3) (1, 4) (1, 5)

First dice is 2: (2, 1) (2, 2) (2, 3) (2, 4)

First dice is 3: (3, 1) (3, 2) (3, 3)

First dice is 4: (4, 1) (4, 2)

First dice is 5: (5, 1)

That is total 15 cases of desirable outcome.

Probability is the number of desirable outcomes divided by the size of the sample space. Therefore, P(<7, 2 dice) is 15/36 = 5/12.

(There is a more elegant method, but there are so few cases that I'd rather count all of them.)