Answer: 36
Step-by-step explanation:
There are 36 possible pairs, all equally likely, corresponding to the entries in the table. Of these, 4 possibilities (marked with an ×) have sum 9, so the probability is 4/36 = 1/9.
(b) The given information has excluded some of the outcomes in the table; in fact only the 10 shaded squares can occur. Of these, 2 possi- bilities have sum 9, so the probability is 2/10 = 1/5.
It’s important to understand what happened here. We calculated (a) as the proportion of the 36 (equally likely) possibilities that are success- ful. We calculated (b) also as a proportion, except the effect of the information was to restrict our attention to a subset of the possibilities.
That’s how conditional probability works—some information is given in terms of a condition that must hold and we identify the subset of the possibilities that satisfies the condition, and then solve the problem using that as our “universe.”
