4 We roll a pair of dice What is the probability that a the

4.) We roll a pair of dice. What is the probability that:

a.) the sum of the pips on the top face is 5?

b.) the sum of the pips on the top faces is 11?

Solution

4.) We roll a pair of dice. What is the probability that:

a.) the sum of the pips on the top face is 5?

Sum 5 occurs in 4 times

P( sum 5) =4/36 =1/9

b.) the sum of the pips on the top faces is 11?

Sum 11 occurs in 2 times

P( sum 11) =2/36 =1/18

Here are all 36 possible rolls with a pair of dice:

(1,1) (1,2)   (1,3) (1,4)   (1,5) (1,6)

(2,1) (2,2)   (2,3) (2,4)   (2,5) (2,6)

(3,1) (3,2)   (3,3) (3,4)   (3,5) (3,6)

(4,1) (4,2)   (4,3) (4,4)   (4,5) (4,6)

(5,1) (5,2)   (5,3) (5,4)   (5,5) (5,6)

(6,1) (6,2)   (6,3) (6,4)   (6,5) (6,6)

Their sums are

2      3       4      5      6      7

3      4       5      6      7      8

4      5       6      7      8      9

5      6       7      8      9     10

6      7       8      9     10     11

7      8       9     10     11     12

Sum 5 in 4 times

Sum 11   2 times