Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two dice are rolled. Find the probability that the sum is , and the probability that the sum is at most .
List the outcomes in order: two coins give (HH, HT, TH, TT), three coins , and two dice pairs (red, blue). Then . For "at least one", use .
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. A sum of . , , , : outcomes, so .
Step 2. At most . Sum : way. Sum : ways. Sum : ways. That is outcomes.
Step 3. The probability. .
Answer: and .
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