Math 125 finite modeling

Question

Roll 2 dice and add the results.

What is the probability of getting an Odd result or a result from 3 to 7?

Answer 1

roll 2 dice, add the results, they sum to 2 to 12

that's 11 different possible outcomes: 2,3,4,5,6,7,8,9,10,11,or 12

that's 6 even and 5 odd outcomes

which might make you think getting odd is less likely than even, but that's not true

one way to get 2

two ways to get 3 (1,2) or (2,1)

three ways to get 4 (2,2), (1,3) or (3,1)

four ways to get 5 (1,4)(4,1),(2,3) or (3,4)

five ways to get 6 (3,3), (1,5),(5,1), (2,4) or (4,2)

six ways to get 7 (4,3),(3,4), (2,5),(5,2), (1,6) or (6,1)

five ways to get 8 (2,6), (6,2), (3,5), (5,3) or (4,4)

four ways to get 9 (3,6), (6,3), (4,5) or (5,4)

three ways to get 10 (4,6), (6,4) or (5,5)

two ways to get 11 (5,6) or (6,5)

one way to get 12 (6,6)

36 different outcomes

two 3's, four 5's six 7's, four 9's and two 11's= 18 ways to get an odd outcome

also 36-18= 18 ways to get an even outcome

50% chance of an odd outcome

ways to get a 3 through 7 = 18 different ways plus ways to get 4 and ways to get 6 = 18+3+5 = 26

26 ways out of 36 to get either an odd outcome or a 3 through 7

26/36 = 13/18

Probability of odd or 3 through 7 = 13/18 = 0.7222... = 72 2/9 % = about 72.2%