A school workshop builds a die with a weight hidden inside, so its faces are not equally likely…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A school workshop builds a die with a weight hidden inside, so its faces are not equally likely. After many throws, the students decide that the chances of the faces to are , , , , and . First check that these six numbers can be the probabilities of the faces. Then find the probability that a throw shows an even number, a prime number, and a number of at least .
Need a reminder? The key ideaShow
For equally likely outcomes, . In general the probabilities of the simple events are at least and add up to , and . For at least one, use . Odds of in favour mean .
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 check. All six numbers are at least , and . So they can be probabilities.
Step 2. Even. The faces are , and : .
Step 3. Prime. The faces are , and : .
Step 4. At least 5. The faces are and : .
Answer: the total is , the chance of an even number is , of a prime is and of at least is .
Watch out. Counting faces would give for even, which is wrong for this die.
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