Three friends go for coffee together every week. They have a tradition that one of them pays for all, based on the following game. They each flip a coin. If two coins match but not all three, then the odd person out pays. If the three coins match, then they flip again (and continue until they all match). On average, how many times do they need to flip before they know who pays?

Question

Mathematics

Keesha

18 September, 18:09

Three friends go for coffee together every week. They have a tradition that one of them pays for all, based on the following game. They each flip a coin. If two coins match but not all three, then the odd person out pays. If the three coins match, then they flip again (and continue until they all match). On average, how many times do they need to flip before they know who pays?

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Answers (1)

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Elisha Rocha · Answer 1

3 times

Step-by-step explanation:

The total number of flips for each round is;

First flip + Second flip + Third flip = 3 flips

Average = [ext]Number of flips/Round[/ext]

Average = 3/1

Average = 3 times.

Check:

Suppose they all match at First and Second rounds,

Average = [ext]3 * 3 / 3[/ext]

Therefore, average = 9/3

Average = 3 times