Question

"If you roll two fair six-sided dice, what is the probability that the sum is 5 or lower?"

Please give me an answer and explain...

Answer 1

sample space=36,
events possible are
1,1
1,2;2,1
1,3;3,1
1,4;4,1
2,2
2,3;3,2 total 10 so probability=10/36=5/18

Answer 2

Given, Number of dice thrown = 2.

Total possible outcomes n(S) = 6^2

                                                 = 36.



Let A be the event of getting a sum of 2. 

n(A) = {1,1}

        = 1.


Let B be the event of getting the sum of 3.

n(B) = {1,2},{2,1}

        = 2.


Let C be the event of getting the sum of 4.

n(C) = {1,3},{3,1},{2,2}

        = 3.


Let D be the event of getting the sum of 5.

n(D) = {1,4},{4,1},{3,2},{2,3}

        = 4.



Let E be the event of getting the sum of 5 or lower.

n(E) = n(A) + n(B) + n(C) + n(D)

        = 1 + 2 + 3 + 4

        = 10.


Therefore the required probability P(E) = n(E))/n(S)

                                                                  = 10/36

                                                                  = 5/18.



Hope this helps!