Question

5. Two dice with six faces are rolled, find the sample space and number of elements in the sample space. Also calculate the probability that the sum of the two faces is equal 6.

Answer 1

Sample space is

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

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

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

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

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

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

Total possible outcomes are 36

The favorable outcomes of  the sum of the two faces is equal 6 are $(1,5),(2,4),(3,3),(4,2),(5,1)$

Probability of  the sum of the two faces is equal 6 is $\frac{5}{36}$