A bag holds five tokens numbered 1 to 5…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A bag holds five tokens numbered to . A player takes out two tokens in one of three ways. In way the player takes a token, notes its number, puts it back and takes again. In way the first token is not put back, and the order of the two tokens is noted. In way the player takes two tokens together. For each way, find the number of outcomes in the sample space. Then find how many outcomes in each way have both tokens with even numbers.
Need a reminder? The key ideaShow
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.
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. Way 1. Any token can come each time: outcomes. The even ones are , , and , which is .
Step 2. Way 2. The second token cannot repeat the first: outcomes. The even ones are and , which is .
Step 3. Way 3. The order is ignored, so each pair is counted once: outcomes. The only even pair is , which is .
Answer: , and outcomes, with , and of them having both tokens even.
Check. Way is way with each pair counted in both orders: . The even count also doubles, from to .
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