Lesson 5 of 16
Count the slips, not the numbers
Show on a big screenA jar has 6 paper slips: 1, 1, 2, 2, 3, 4. You pick one slip without looking. A student says, "4 numbers, so P(1) = 1/4." Is that right?
Step 1 of 4
- 6 slips in the jar: 1, 1, 2, 2, 3, 4.
- Two slips show 1.
- P(1) = 2/6 = 1/3.
- Not 1/4. Count slips, not numbers.
What is one outcome?
You pick one slip. So each slip is one outcome. The slips look alike and you pick without looking. So all 6 slips are equally likely. Each has the same chance.
The numbers are labels on the slips. Two slips can carry the same label.
| Jar | Question | Count slips (right) | Count numbers (wrong way) |
|---|---|---|---|
| 1, 2, 3, 4, 5, 6 | P(1) | 1/6 | 1/6 |
| 1, 1, 2, 2, 3, 4 | P(1) | 2/6 = 1/3 | 1/4 |
| 1, 1, 2, 2, 3, 4 | P(less than 3) | 4/6 = 2/3 | 2/4 = 1/2 |
In the first jar no number repeats. So both ways agree. In the second jar numbers repeat. Repeats make the two ways differ.
Pick from the second jar 60 times. A 1 comes about 20 times. That is about 1 in 3, not 1 in 4.
Now try it. Count the slips in three jars. Tap the right chance.
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Try the lab to finish this lesson.