# Forum

#### If you flipped three pennies, what would be the odds that they all came out the same?

wolgang

Oct 13, 2008 6:27pm

2/8 or 1/4 = 25%. 3 coins = 3 bits = 2^3 = 8 possible choices all coins have same orientation = HHH or TTT so 2 choices Thus 2/8 This is a very CS way of looking at it :p
kumarsalib

Jan 4, 2009 6:39am

I love when people ask for their perfect match to have the same answer and then they answer it wrong themselves.
RandomGod

Jan 4, 2009 8:32am

So far you're all wrong. The odds that they all came out the same is 100%.

This is specified right in the question. They all came out the same. It says so, right there. And, since it's in the past, it will not change. So, 100% chance that is the thing that happened.
austensibly

Apr 30, 2009 9:18am

Everyone's coming out experience is different.
longbondsilver

Apr 30, 2009 10:28am

All y'all's a bunch of haters: ask each penny and they'll tell you they are unique. So the probability is zero that the outcomes are all the same. Otherwise you can get either HHH (1/8) or TTT (1/8) as long the pennies are flipped with an equal probability outcome...binomial and all that. In any case 2/8 or 1/4.
JaronK

Apr 30, 2009 10:51am

Man, that's a lot of people guessing 1/8, which is the possibility of them being all heads, or being all tails. But the question was about the possibility of them all being the same, so all heads and all tails are both valid. Thus, you get 1/8+1/8, or 1/4. However the question is defective... the answers are all written in probability (1 in 4) but the question asks for odds, which would be 3 to 1.

Apr 30, 2009 1:30pm

2 in 8.
senbonz

May 9, 2009 4:29pm

Definition of probability: P = (# favorable outcomes)/(# all possible outcomes); or P = n/m n = 2 (they could all be heads, or they could all be tails) m = (2)^3 = 8 Therefore: P = (2)/(8) = 1/4
moocrazy

Jun 14, 2009 6:07pm

It seems there are four possible outcomes: HHH, TTT, HHT, HTT. The order would not be important. Since both HHH and TTT are "the same," that looks like a 2 out of 4 probability, (1 out of 2) which is not one of the possible answers. Maybe it's too late at night and I'm half asleep. What is wrong with this answer?

Jun 14, 2009 7:43pm

You're missing four possible outcomes. It should be these eight: HHH, TTT, HHT, HTH, THH, HTT, THT, TTH.

dooglus

Jun 15, 2009 1:01am

When I play the lottery there are 2 possible outcomes: I win, I don't win.  So that looks like a 1 out of 2 probability of me winning?

The problem is that these two outcomes aren't of equal probability.  In your list, HHH and TTT happen one time in 8, but HHT and HTT each happen 3 times in 8, so you can't just say it is "2 out of 4".  You need to count each of the 3 ways that HHT and HTT can happen, giving a true probability of "2 out of 8".

xvegangirlx

Jun 15, 2009 9:16am

If you toss 3 coins like that, you can do an I-Ching reading.

Since I have done this quite often, I have to say that many times all 3 coins are the same. I don't know what the odds are, but it happens often. When they are all heads, that's a straight line for each, and if not its a broken line.......six lines make up a hexagram, and then you consult an I Ching book for the answer.

Phil42

Jun 15, 2009 7:51pm

If you flip three pennies, it's pretty close to a 100% probability that they will all still come out pennies, therefore all three will be the same.

On a more serious note, the phrase "came out the same" is a bit vague, it _could_ imply all heads or all tails - or specifically just all heads (or all tails).

DiscoJer

Jun 15, 2009 8:05pm

^ It's meant to be like that, be a trick question.  People think 1 in 8, when it's really 2 in 8.

But that's not quite right either, because sometimes they can land on their edge. Pretty rare, but possible.

xvszero

Jun 15, 2009 8:12pm

I often feel pretty interchangeable at work (programmer) but the fact that some people seem to actually be struggling with this makes me think maybe I am decent at my job after all.

xvegangirlx

Jun 16, 2009 2:14pm

I used to study the I ching and do many readings, so I was often tossing 3 pennies and recording the results. All 3 landing the same way, either as heads or tails, happened quite often.

Of course, this was not just a matter of odds, as the way the coins fall is being directed by the supernatural realm while doing an I ching reading.

dooglus

Jun 16, 2009 8:24pm

Are you sure that the coins were being directed by the supernatural realm?  I only ever did one I ching reading, so I don't have enough evidence to go on, but my gut tells me that when I flip coins the outcome is effectively random, not directed by any kind of supernatural force.  To be able to say "of course" about such an extraordinary claim seems amazing to me.

xvegangirlx

Jun 17, 2009 10:08am

An I Ching reading is very different then just flipping coins....it is a form of divination.  You can use yarrow rods instead of coins, either way it is still metaphysical.

LeTinctoire

Jul 6, 2009 12:37am

It's relatively amusing how many people answer something else than 1/4. It's not that hard. It seems to me that people are forgetting there are two ways in which the coins "[come] out the same": all heads and all tails.

Suppose that you'd flip three pennis in a row(!), then there are eight scenarios that might happen (TTT, TTH, THT, THH, HTT, HTH, HHT, HHH), of which two (TTT, HHH) are "all the same". Two out of eight is 1/4.

LeTinctoire

Jul 6, 2009 12:55am

Hurr durr, how redundant. And wrong. As stated earlier, odds is the quotient of probabilities. In this case it's 2/8 versus 6/8, so 1/3.