Question

A pair of dice consisting of a six-sided die and a four-sided die is rolled and the sum is determined. What is the probability that the sum of the faces is 5 or 7 or 8 or 9 given that i. the first outcome was a 4? ii. the first outcome was greater than 2? iii. the first outcome was a 1? iv. the first outcome was less than 4?

Answer 1

in all four situations, the first outcome is fixed. so focus on the possible outcomes of the second, four-sided die

i. if the first outcome was a 4, and the sums being considered are 5, 7, 8, and 9, then it naturally follows that 1, 3, and 4 are the necessary outcomes on the second dice. (4+1, 4+3, 4+4. note that 9 is an impossible outcome.). find the probability associated with getting these three possible outcomes out of 4 total.

ii. if the first outcome was "greater than 2" that means the first die could have been 3, 4, 5, or 6. find the # of possible combinations that add up to 5, 7, and 8. (ex: 3+2, 3+4, etc.)

iii. similar logic. if the first outcome was 1, count the number of outcomes on the second die that could lead to 5, 7, 8, or 9

iv. similar logic. if the first outcome was less than 4, that means the first number could be 1, 2, or 3. count the number of outcomes on the second die that could lead to 5,7,8 or 9.