What is wrong with this?

Calvin Edit: Discussion about a problem should occur on the solution itself. I have transformed this note into a "solution", and locked the note.

I recently tried this problem but did not get the correct answer.Here is my approach: Five consecutive coins can be chosen in 15 ways.Let us say we choose the first 5 coins.The probability that all of them show heads is $\dfrac{1}{2^5}$ .Because we want exactly 5 consecutive heads the other 15 coins should show tails,the probability of that is $\dfrac{1}{2^{15}}$ .Thus,probability of 5 consecutive heads is $\dfrac{1}{2^{20}}*15$ . WHAT IS WRONG?

#Combinatorics #Probability #HelpMe! #Pleasehelp #Calvinlin

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

The error lie in the fact that when you say we want exactly 5 consecutive heads then the other 15 coins need not show tails, the question simply demands for at least one line of exactly 5 succesive heads somewhere in the string of 20 results. Rest can be anything.

Ronak Agarwal - 6 years, 3 months ago

Oh my god!!Thank you.Such a foolish mistake I was making!!Now,I would be able to solve every problem like this!!Thank you!!

satyendra kumar - 6 years, 3 months ago

Can you add your solution to the problem? Thanks

Calvin Lin Staff - 6 years, 3 months ago

@Azhaghu Roopesh M @Ronak Agarwal help!

satyendra kumar - 6 years, 3 months ago

Satyendra, ideally discussion about a problem should occur on the problem itself, instead of linking out to a note. This allows other people who made an identical mistake on the problem to be able to easily identify it, and learn from you.

I have created a "solution" on the problem, as that we can have this discussion there. As such, I have locked this discussion.

Calvin Lin Staff - 6 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$