You are invited to Log in or Register a free Frihost Account!

# Math Problem

_AVG_
I was having difficulties trying to solve a Math Problem.

Here it is:

IF FOUR PEOPLE TOSS A COIN, WHAT IS THE PROBABILITY OF THE FOURTH PERSON TOSSING A TAIL?
ninjakannon
The probability is 0.5, unless you've worded your question wrongly. You have stated a probability that is independent to the other results, therefore the probability is the same as it would be if there were one person tossing the coin.

Are you sure you mean something so simple?
Arnie
When asking such a question, always explain your thoughts about it and at what point you can't figure it out. That way the person answering can help you understand the problem better. Currently, we don't know why you think this is so hard, as ninjakannon stated... are you confused by the fact that there are 3 others tossing a coin? Because that has no influence - even in the less likely event that the 3 others get tails, the chance for the fourth to get tails is still 0.5.
WhistleTurning
The only slight difficulty comes if the last toss following 3 tails has to also be a Tail, but this is still quite easy .5x.5x.5x.5=0.0625. If you had to write down all the possible outcomes with a tail at the end then there are 8
Yazz
Jeeze, probability is such messy business.

I agree, if you have a 4 coins, their probabilities are all independent of each other. They aren't a single system. If there was a single coin and 4 people flipped it, the probability would depend upon the previous 3 throws.

Of course, probability is a bunch of randomness if you ask me. You can flip a coin until you have an equal turn out of heads and tails, but if you toss it twice more and get two heads, the equality is ruined, and may be ruined for infinity tosses afterwards.

Probability is so... philosophical...
rvec
 Yazz wrote: Jeeze, probability is such messy business. I agree, if you have a 4 coins, their probabilities are all independent of each other. They aren't a single system. If there was a single coin and 4 people flipped it, the probability would depend upon the previous 3 throws.
No it wouldn't. The only way the probability would depend on the other 2 was if you wanted 3 or 2 heads/tails.
 Yazz wrote: Of course, probability is a bunch of randomness if you ask me. You can flip a coin until you have an equal turn out of heads and tails, but if you toss it twice more and get two heads, the equality is ruined, and may be ruined for infinity tosses afterwards. Probability is so... philosophical...

It's not random or philosophy , it's math
newsarific
The bit about the other 3 coins being tossed is probably just to trick you into doing the question the wrong way.
ThePolemistis
 _AVG_ wrote: I was having difficulties trying to solve a Math Problem. Here it is: IF FOUR PEOPLE TOSS A COIN, WHAT IS THE PROBABILITY OF THE FOURTH PERSON TOSSING A TAIL?

Each person is independant of the other person, so it doesnt matter what person 1, 2 or 3 toss since it will never affect the forth person.

Therefore, under normal conditions for forth person to toss a tail is 0.5 or 50% probability.
Soulfire
Not to beat a dead horse, but probability is something we hit really hard in math class last year. When two or more events are independent, it means that the events in no way rely on the outcome of other events.

So if Person 1, Person 2, Person 3, and Person 4 all flip coins ... none of the outcomes are dependent upon the results of each other.

Therefore, as we know, the probability remains .5 or 50% (the other .5 being a 'heads'). Basically, they worded the question awkwardly to distract your thoughts. Story problems and the like always throw more information at you than you really need to solve the problem.
_AVG_
Is there any formula or something to work it out?

And by the way, the exact question is as follows:
Four People Each Toss A Coin. What is the Probability that the Fourth Person Will Toss A "TAIL"

The question also had four options:
A. 1/2 B. 1/4 C. 1/8 D. 1/16
Yup, it's as easy as everyone said... the answer is A. 1/2

since the 4th person is completly independent, the possible outcomes for the 4th person are either heads or tail.
tijn01
0.5 .... it is either tails, or heads............ 2changes --> 1 / 2
can't get much easier than this
hack_man_
 newsarific wrote: The answer is definitely 0.5. The bit about the other 3 coins being tossed is probably just to trick you into doing the question the wrong way.

Yeah, it is all just out to confuse you into doing something wrong. As soon as I read a question, I write the useful info and simply ignore the rest...
otiscom
Yep definitely 50% chance of heads or tails.

As said none of the others can influence the outcomw.
ninjakannon
 _AVG_ wrote: Is there any formula or something to work it out? And by the way, the exact question is as follows: Four People Each Toss A Coin. What is the Probability that the Fourth Person Will Toss A "TAIL" The question also had four options: A. 1/2 B. 1/4 C. 1/8 D. 1/16

The answer's definitely 'A' - thanks for posting the question, now we can answer for definite.

You want a formula to work it out?

If we say:
x = number of elements in the subset you are focusing on - In this case 1, tail.
n = number of elements in the set - In this case 2, head and tail.

P(x) = x/n

Probability(tail) = number of tails over (or divided by) total number of options
P(tail) = 1/2
= 0.5
0.5*100 = 50% (if you want it as a percentage).

This is very simple probability. It gets a little more complicated when looking at the probability of one event happening given that another happens also etc.

I hope this helps!
PIbrothers
The probability is 1/2, I think.
mathiaus
As this has been answered (and then repeated many many times!), I'll close it now.
PM if for any reason you need it re-opened.

-close-