Coin tossing (yet another)
You flip two coins simultaneously. If one coin is heads, what is the probability that the other coin is heads?
Labels: logic
posted by Chris at
9:34 AM
Wednesday, September 30, 2009
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31 Comments:
2 coins at the same time?
there can be only 3 outcomes.
-2 heads
-2 tails
-1 of each
making it 33.3%
Hi Knightmare. Interesting, you got the right probability, but the wrong explanation. I shall assume that you were in a hurry to be the first post. Would you care to try again?
I tried it myself, and found another outcome!!
2 heads
2 tails
first heads & second tails
first tails & second heads
And the other?
Unknown because the coin hit the floor, rolled under the couch.
Hint: Flip quarters, not pennies. Moving the couch to much work for a penny.
What is the probability of the coin rolling under the couch and being heads up?
Dont matter if there R 2 or 100 coins. The probability for one of them to be head is 1/2
Hi Torres, that's not what the question asked.
wouldnt each coin that is flipped be its own separate event? maybe i misread the question but how i read it it would be 50/50. i think though you are asking what is the probability that it will come up heads and heads, in that case it would be 33.333...% of the time.
let me elaborate on that previous post. one coin would have no effect on the other, just like roulette and the history board, if you see there has been 10 black spins the chances are still the same on the next spin that it will come out black or red
Twice in one blog! - right answer, wrong explanation. What's the probability of that happening?
The probability of getting heads and heads is only 1/4. But the answer I want to see explained is 1/3.
The question gave us that the first coin is heads, therefore it is a 50-50 chance that the second coin will be heads.
Anonymous, you haven't read the question correctly.
Each coin, independently has a 50/50 chance of being heads.
But I think Chris is refering to a different scenario. I had a hard time comphrending a previous ToM where I showed to myself an outcome I did not think was possible. It was so hard to understand, I think I quickly forgot it.
How about if you flip nine coins, and they all are tails, what is the probability that the tenth one would be tails also. I would say it's 50/50, (it's indepentent), but if you were asked before you flipped any, what is the probability that they all will be tails? That's not 50/50.
I may be completely wrong.
Chris? I added a comment to "what a shot" to lay out how I think the probility should work. Can you compute how you would do it, given the path I suggested?
Hi Ragknot. As you've asked I'll take a look at your prob.
You have correctly answered the probability problem that you asked.
Time to move on.
There are four equally likely outcomes: HH, HT, TH, TT. The last must be excluded as we know that at least one is a head. That leaves HH, HT, TH. So there is a 1/3 chance of HH.
hi Chris
does timing/order matter?
what i mean is-are heads/tails and tails/heads two separate outcomes or just one?
Hi Knightmare. Timing and order don't matter. You can even use one coin in two tosses. I could have phrased the question as: If you toss a coin twice, and heads comes up on (at least) one toss, what is the probability that the other is heads also?
I see that your post and my previous one were nearly at the same time, so I guess you hadn't seen it when you posted.
This is covered in basic Prob/Stats class in high school.
P(A given B)= P(A and B) / P(B)
In this case, A is Head/Head, and B is first head.
So, P(A given B)= (1/4)/(1/2) = 1/2
Your logic is just a bit off, as is your reasoning, but for someone who hasn't taken prob/stats, it seems correct.
Hi previous anon,
Not quite.
A is actually head on either trial, so P(A)=3/4
That means
P(A given B)= (1/4)/(3/4)= 1/3
Hi Anonymous. The correct expression is:
P(H¦H)=P(HH)/(P(HH)+P(HT)) = (1/4)/((1/4)+(1/2)) = 1/3.
I didn't present it that way as it is unnecessarily technical. My HH, HT, TH reasoning is far easier to understand.
I have done advanced statistics - but a long time ago.
Anonymous 2:57 PM, Sorry, I didn't mean to gang up on you. My post crossed with the last Anonymous's.
You are all stupid. it is 50/50..you get either heads or tails. Its not that hard people!
-Amanda
Amanda. Clearly the problem is too hard for you. So is being civil. The correct answer is 1/3. This is a well known problem. I wouldn't have posted it if the answer was 1/2.
Jake. I deleted your post. There is absolutely no need for that kind of language especially as I posted the problem and I've presented the solution twice already. I'm the MC. So what does that make you?
ok, goin g back to my early highschool algerbra classes here. each coin has an 50:50 chance of getting heads so that would be 1/2, rite? so because its two coins here, u would multiply 1/2 by 1/2 and get 1/4. thus, ur probibility
let me no. jesusfreakalloftheway@yahoo.com
oh dang! i just redid the math, it would be 1/3. sry about that. =D could someone go over the steps tho, i would like to know just how the problem works. its sad tho, its such a common problem and i got it wrong. =[
jesusfreakalloftheway@yahoo.com
jesus..., I have alrady posted two "explanations".
Chris, I beleive the reason many people are having problem with this is because the question is poorly worded. If you were to state "if one of the two coins is heads", it would seem easier. The way I think people are reading it (as I did for a while) is that if the first coin you see is heads what is the odds the other one is, in which 50% is the correct answer. So there is no need to be harsh on people who misread the question.
Hi Adam, I accept that I could have changed "one of the coin is heads" to "one of the coins is showing heads" etc. That the coins were flipped simultaneously precludes that there was a first or second coin. Realising that it could be either coin is an key part of the problem. I considered all of that when I posted it.
The only two people I was harsh with were Amanda and Jake. I deleted Jake's post as it broke the kid sister rule (it also made completely ridiculous accusations and suggestions). I rebuked Amanda for being insulting. I was particularly hard on her as the correct solution, with reasoning, had been presented several times when she posted.
since there are 2 coins there are 4 sides, since 1 heads is already down that leaves 3 sides, 2 chances at tails 1 chance at heads, hence the 33.3*%
Sorry i explained that horribly and i must appologise because The comments didn't load for me earlier so i was unaware that it had already been answered.
H Anonymous. I can't get my head round your explanation. But it gives the right answer, and also does so in more complex situations. I find that very interesting a/o curious.
What if the coin landed on it's side? (Neither H nor T)
H - Head
T - Tail
S - Side
So we have HH, HT, TT, TH, HS, SS, SH, ST, TS
So probability is 0.11111111...etc
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