# Thread: Can you solve this Probability ?

1. ## Can you solve this Probability ?

You work at an ice cream stand that offers 8 different flavors. On a busy day, you take requests for one-scoop cones from 6 people, but forget the flavors. How many flavors do you have to remember for the probability that you randomly get all the other flavors correct on the first try to be greater than 0.01? Explain.

2. Hello, jessicap!

I have a back-door approach . . .

You work at an ice cream stand that offers 8 different flavors. On a busy day,
you take requests for one-scoop cones from 6 people, but forget the flavors.
How many flavors do you have to remember for the probability that you randomly
get all the other flavors correct on the first try to be greater than 0.01?

If you remember all 6 orders, your probability is 1 . . .
greater than 0.01

If you remember 5 of them, you must guess on the sixth order.
. . You will be right with probability: $\tfrac{1}{8} \:=\:0.125$ . . .
greater than 0.01

If you remember 4 of them, you must guess on the other two orders.
. . You will be right with probability: $\left(\tfrac{1}{8}\right) \:=\:0.015625$ . . .
greater than 0.01

If you remember 3 of them, you must guess on the other three orders.
. . You will be right with probability: $\left(\tfrac{1}{8}\right)^3 \:=\:0.001963125$ . . .
less than 0.01

Therefore, you must remember at least 4 flavors.

3. Thanks for your time and effort. My boy took your solution into his teacher, and she said that it was wrong. He didn't get the right solution today though. I'll see if he can get his hands on it, and I'll let you know what she is saying the answer is.