Maya answers three quiz questions in a row…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Maya answers three quiz questions in a row. The chance that she gets the first one right is . After a right answer, the chance that she gets the next one right is . After a wrong answer, her confidence drops, and the chance falls to . Draw the tree and find the probability that she gets all three right, the probability that she gets exactly two right and the probability that she gets at least one right.
Need a reminder? The key ideaShow
The multiplication rule is . In a tree diagram, multiply along each path and add the paths that make the event. Without replacement, the second-stage branches use the changed contents.
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 tree. Write R for right and W for wrong. The branches are in the picture, with the probability of each step given the earlier answer.
Step 2. All three right. RRR: .
Step 3. Exactly two right. RRW: . RWR: . WRR: . The sum is .
Step 4. At least one right. The only way to get none is WWW: . So the answer is .
Answer: , and .
Watch out. The second and third factors are not the same on every path. Read each one from the branch that leaves the earlier answer.
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