Question

Suppose you roll two fair dice. See the sample space on screen to represent the situation then

determine each of these probabilities.

a. Getting doubles

b. Getting an even sum of at most 6

c. Getting doubles or an even sum of at most 6

d. Getting doubles and an even sum of at most 6

Answer 1

Explanation:

Each die has 6 outcomes. So there are a total of 6×6=36 possible combinations.

`\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&1+1&1+2&1+3&1+4&1+5&1+6\\2&2+1&2+2&2+3&2+4&2+5&2+6\\3&3+1&3+2&3+3&3+4&3+5&3+6\\4&4+1&4+2&4+3&4+4&4+5&4+6\\5&5+1&5+2&5+3&5+4&5+5&5+6\\6&6+1&6+2&6+3&6+4&6+5&6+6\end{array}\right]`

a. There are 6 possible doubles. So the probability is 6/36 = 1/6.

b. There are 9 possible even sums less than or equal to 6. So the probability is 9/36 = 1/4.

c. There are 6+9−3=12 possible doubles or even sums less than or equal to 6. So the probability is 12/36 = 1/3.

d. There are 3 possible doubles that are sums less than or equal to 6. So the probability is 3/36 = 1/12.