In a throw of 2 fair dice, there are 6*6=36 equiprobability outcomes.
To get a sum of 5, there are 4 ways, (1,4),(2,3),(3,2),(4,1) with probability of 4/36=1/9
To get at least one 5, there are 6+6-1=11 outcomes (note (5,5) has been counted in both, so subtracted from sum). The probability is 11/36
Since the two events are mutually exclusive (once we have a five, the sum can no longer be 5), we can add the probabilities to get the probability of one event or the other.
P(sum of 5 OR at least one 5)=1/9+11/36=4/36+11/36=15/36=5/9
For Wyatt's recipe the rate is: r1 = 3.15 / 9 r1 = 0.35 For Cora's recipe the rate is: r2 = 2.4 / 8 r2 = 0.3 The difference between both recipes is: r1-r2 = 0.35 - 0.3 = 0.05 Answer: 0.05 cups of flour per shortcake less is needed for Cora's recipe
