# Coin is tossed 3 times

1. Jan 10, 2009

### tictac123

Qst A).

A coin is tossed 3 times and you note that the coin lands heads exactly twice. What is the probability that the first toss was the tail?

I know how to do it logically but not with all the notation.

Any help appreciated.

Thanks

Last edited: Jan 10, 2009
2. Jan 10, 2009

### HallsofIvy

Staff Emeritus
Re: Probability

That trick didn't work when you posted this in "homework"- it won't work here!

3. Jan 10, 2009

### mathman

Re: Probability

It looks like the answer should be 1/3, since there is nothing to favor any one of the three tosses over any other.

4. Jan 11, 2009

### HallsofIvy

Staff Emeritus
Re: Probability

If the problem had said "what is the probability the first coin was a tail" would you also answer "1/3"? Since "heads" or "tails" is all there can be, what does the remaining "1/3" probability represent?

tictac123, since you say you were able to do this "logically", what answer did you get?

5. Jan 11, 2009

### mathman

Re: Probability

Since the condition is that 2 tosses came up heads, the probability that the first toss was heads is 2/3.

6. Jan 12, 2009

### HallsofIvy

Staff Emeritus
Re: Probability

There are 8 possible outcomes for three coins, and you can list them:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Of those, exactly 4 have two "H"s, HHT, HTH, and THH. Of those 3, 2 have "H" first.

I would still like to know what tictac123 means by "I know how to do it logically but not with all the notation."

7. Jan 12, 2009

### NoMoreExams

Re: Probability

A solution exists?

8. Jan 15, 2009

### regor60

Re: Probability

9. Jan 15, 2009

### NoMoreExams

Re: Probability

No 4 have 2 heads, HHH, HTH, HHT, THH. Out of them 3 have exactly 2 heads

10. Jan 16, 2009

### Niles

Re: Probability

It's 1/3. You can even use Bayes' sentence, but it might be overkill in this case since HallsofIvy's list says it all (but it's a good exercise to double-check it using Bayes' sentence).

11. Jan 20, 2009

### regor60

Re: Probability

Who are you quibbling with, him or me ? He cites three as evidence of four. Obviously the issue is whether the intention was exactly two heads or two or more heads, but I'm just referring to his statement

Last edited: Jan 20, 2009
12. Jan 20, 2009

### NoMoreExams

Re: Probability

Probably you since to me "exactly 3 have 2 heads" doesn't mean exactly 2 heads since you put "exactly" before the 3.