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Three fair coins are tossed. List all the outcomes, and find the probability of (a) three heads…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Three fair coins are tossed. List all the outcomes, and find the probability of (a) three heads, (b) exactly two heads, (c) at least one head.
Need a reminder? The key ideaShow
List all the equally likely pairs and count. For events that do not affect each other, multiply. For at least one, take the chance of none from 1. Without putting back, the second chance changes.
The worked solution
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. The outcomes. HHH, HHT, HTH, HTT, THH, THT, TTH, TTT: in all.
Step 2. Three heads. Only HHH: .
Step 3. Exactly two heads. HHT, HTH, THH: .
Step 4. At least one head. .
Answer: , and .
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