Golf balls

Maria collects logo golf balls. She keeps them in a huge bin. She wants to know how many she has, but she doesn't want to count them all. She gets an idea. She takes 50 out of the bin and marks them with a small red dot. She then replaces the golf balls and mixes all the golf balls in the bin. Maria then asks her younger brother to close his eyes and pick 30 golf balls from the bin. Of the 30 taken, 17 have the small red dot.

What do you think of Maria's idea? Can she estimate how many golf balls are in the bin?

Alternatives

You might put pieces of tape on 50 bingo chips, mix them in with 40 unmarked chips, and have students draw out 30 and count the number that are marked.

Approaches

No, there's not enough data. (No reason.)

Why?

No, there's not enough data; you can't be sure the balls are properly mixed or that the sample is random.

What if we assumed they were?

Yes, there's enough data. Apparently there are 13 unmarked balls in the hat, so add 13 to the 50 marked balls and you get a total of 63.

Can you draw a picture representing the situation?

No, there's not enough data; we don't know whether the younger brother replaces each ball after drawing it out.

How does that make a difference? Can you solve it both ways? How confident are you in your results?

Yes, there's enough data. 30/17= x/50, where x is the total number of balls. So x is about 88.

Why?