# Math Help - Probability

1. ## Probability

Hi all =)

Question...
A fair coin is tossed thrice. Supposed we denote a "head" turning up as 1 and
"tail" as 0. Given that the total on all three tosses is an odd number,
what is the probability that at first toss, we get a "head"?

i dont have any idea to start answering this question..
please guide me.. =)

2. Originally Posted by nameck
Question...
A fair coin is tossed thrice. Supposed we denote a "head" turning up as 1 and
"tail" as 0. Given that the total on all three tosses is an odd number,
what is the probability that at first toss, we get a "head"?
Here is your outcome set. You count them
$\begin{array}{ccc}
1 & 1 & 1 \\
1 & 1 & 0 \\
1 & 0 & 1 \\
1 & 0 & 0 \\
0 & 1 & 1 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
0 & 0 & 0 \\

\end{array}$

3. Originally Posted by Plato
Here is your outcome set. You count them
$\begin{array}{ccc}
1 & 1 & 1 \\
1 & 1 & 0 \\
1 & 0 & 1 \\
1 & 0 & 0 \\
0 & 1 & 1 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
0 & 0 & 0 \\

\end{array}$
should i use conditional probability?

4. Originally Posted by nameck
should i use conditional probability?
How many odd sums?
How many odd sums start with a 1?

5. Originally Posted by Plato
How many odd sums start with a 1?
four..

6. Originally Posted by nameck
four..
There are four odd sums. How many start with a one?

7. There are four odd sums and there are four start with a one.

8. Originally Posted by nameck
There are four odd sums and there are four start with a one.
That is wrong. Count again.
$\begin{array}{ccc}
1 & 1 & 1 \\
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\

\end{array}$

9. 1 1 1
1 1 0
1 0 1
1 0 0

0 1 1
0 1 0
0 0 1
0 0 0

first four, start with a one.. right?

10. Originally Posted by nameck
first four, start with a one.. right?
No. Of the odd sums how many start with a 1?
That is the idea of conditional probability.
The given narrows the outcome space.

11. i see...
sorry plato.. i'm kinda slow..
the answer is two..
correct?