Question

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 12?

Answer 1

no of outcomes

(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)

total no. of outcomes = 36

probable events = 35

$probability \: = \frac{35}{36}$

Answer 2

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 12?



In the experiment of throwing two fair dice the probability of having 11 or 12 as the
sum of the two numbers that turn up is:
P(x=12) = 1/36, and P(x=11) = 2/36
So, P(x<11) = 1 - [P(x=12) + P(x=11)] = 1 - 3/36 = 33/36 = 0.91666... 
≈ 91.7%