You are given a box of 100 silver dollars, all facing "heads" up. You are instructed to shake the box 3 times; after each shake, you will remove all the dollars that are "heads up" before shaking again. You may keep all the dollars that are still tails up following the third shake. How many dollars will you most likely get to keep?

Question

01-03-2022
Advanced Placement (AP)

contestada

You are given a box of 100 silver dollars, all facing "heads" up. You are instructed to shake the box 3 times; after each shake, you will remove all the dollars that are "heads up" before shaking again. You may keep all the dollars that are still tails up following the third shake. How many dollars will you most likely get to keep?

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zlskfrum zlskfrum · Answer 1 · 2022-03-01T23:32:26+01:00

Answer:

Explanation:

Assume that after each shaking, a silver dollar has an equal chance of "head" or "tail" up.

There will be likely 100/2 = 50 dollar coins with "heads" up. Removing them leaves 50 coins.

Again after the second shakes, 50/2 = 25 coins will likely be "heads" up. Removing them leaves 25 coins.

After the third shakes, approximately 25/2 = 12.5 coins will be "heads" up. Of course there is no 0.5 coin. Rounding up you likely get to keep 13 dollar coins.