Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two dice are thrown together, one white and one black. Asha says that she will list the results by the numbers shown without caring which die shows which number. So for her, the pair and the pair are the same. How many pairs does Asha get? How many outcomes does the sample space have when we keep track of the white die and the black die? Find how many ordered outcomes give a total of , and how many of Asha's pairs give a total of . Explain in the answer why Asha's pairs are not equally likely.
The sample space lists every outcome. Steps that happen one after the other multiply: . From different objects, drawn give outcomes with replacement, in order without replacement and when the order is ignored.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Asha's pairs. The doubles are pairs. The pairs with two different numbers are . In all, .
Step 2. The ordered outcomes. The white die has results and the black die has . So outcomes.
Step 3. A total of 7. The ordered outcomes are , , , , and , so of them. Asha's pairs give only : , and .
Step 4. Why Asha's pairs are not equally likely. Each of the pairs with two different numbers comes from ordered outcomes. Each double comes from . So a total of really takes of the outcomes, and Asha's pairs would make it look like of .
Answer: pairs, outcomes, and and outcomes with a total of . Only the ordered outcomes are equally likely.
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