Coin flip sequences

Probability Level 2

A fair coin is about to be flipped 5 times. Which of these sequences of flips ("H" for heads, "T" for tails) is the least likely to occur?

TTHHT HTHTH TTTTT HHHHT They are all equally likely

Edward Teach by Edward Teach , 34, USA

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1 solution

Edward Teach
Feb 19, 2018

Imagine if this question were worded slightly differently: 

1
2
3
4
5
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7
 
A fair coin is about to be flipped 5 times. Which of these outcomes is the least likely to occur?

[ ] 2 Heads, 3 Tails
[ ] 3 Heads, 2 Tails 
[*] 5 Tails
[ ] 1 Head, 4 Tails
[ ] They are all equally likely

Then, the correct answer would be "5 Tails." However, when considering a specific sequence of coin flips, each sequence is just as likely as the others. It just so happens that there are more sequences that have 3 Heads and 2 Tails than there are sequences that have 5 Tails.

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