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There are 3 coins. When you flip them, at least 2 will land the same way. Does that mean you have a 50% chance of throwing all the coins the same way and it all comes down to the last coin?

Example:

First 2 coins: TT, HH

3rd coin: T, H

Edited by Lemon Drops

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Guest

You would have a 12.5% chance of all three coins landing the same way.

Actually, it's a 25% chance. You have a 12.5% chance of all heads, and a 12.5% chance of all tails.

You have a 50% chance of all coins landing similarly if you are given that the FIRST TWO landed the same, not any two. If the first two land differently, of course, then you will still have two coins landing the same after 3 flips, but a 0% chance of having 3 similar flips.

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Maybe I misunderstand the question.

When you flip them, at least 2 will land the same way
yes it's trivial, it's not a plus condition

the probability of 3 same landings is 25% (assuming that they are normal coins with P(head)=0.5 P(tail)=0.5)

Edited by det

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The spoiler doesn't work for me. The dialog box is way off the left of my screen and I can't see what I am typing.

Taking one case at a time it is true that if you select the two coins that are the same, then 50% of the time the third coin is the same as the other two. If the first two are the same, then there is a 50% probablity that the third one will be the same. If the first and third are the same, there is a 50% probability that the second coin will be the same as the other two. If the second and third coins are the same then there is a 50% probability that the first one is the same as the other two. The trick is that the two cases where all three coins are the same (1 chance in four) is used in all three of these groups.

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There are 3 coins. When you flip them, at least 2 will land the same way. Does that mean you have a 50% chance of throwing all the coins the same way and it all comes down to the last coin?

Example:

First 2 coins: TT, HH

3rd coin: T, H

Seems to me there are 4 possibilities:TTT, TTH,THH,HHH and the order doesn't matter. So 50% chance no matter what.

Gess

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Seems to me there are 4 possibilities:TTT, TTH,THH,HHH and the order doesn't matter. So 50% chance no matter what.

Gess

The order does matter, in a way, cause TTH and THH are more likely to happen than TTT and HHH. When you write TTH you actually includ the chances of TTH, THT and HTT in it. Which makes it three times more likely to happen the either TTT or HHH.

Edited by Arbelle

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Ok now not exactly will there be 2 the same. Let's say you get a side. Heads=H Tails=T Side=S. Side isn't impossible but rare. It's like a 10% chance to get a side. 3.3% of getting 3 sides. Now 87.7% is left. About 11% to get 3 heads or tails. 33% to get 1 tail/head. So like a 25.3% chance to get 3 of the same things.

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SSS HHH TTT is 3 of the same.

SHT SHH SHS is SH, STH, STT, STS is ST. SST, SSS, SSH is SS, Is S.

3x9=27. 27+3=30. 3 out of 30= 1 tenth.

There is a 1 out of 10 chance of getting 3 of the same, 9 of 10 of getting something else. A 10% chance to get 3 the same.

Edited by ThisIsALie

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I dunno where my spoiler went, so Imma write a new one xD

The problem is, which coin is the last coin, and which coins are the first two, so there are actually eight ways of the coins landing (not counting sides):

TTT,TTH,THH,HTT,HHT,HHH,HTH, THT

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The answer is the standard 0.25 probability that you would compute for three fair independent coins.

The OP says that at least 2 will land the same way, which leads one to believe that two specific coins are magically linked and will always mirror the others landing. In fact, all it is saying is the obvious: if you flip three coins, 2 will end up the same.

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