# Probability of a tail followed by 2 heads on a biased coin

• Feb 11th 2013, 10:09 PM
battery88
Probability of a tail followed by 2 heads on a biased coin
Suppose we have a biased coin for which the probability of heads is 3/4 while the probability of tails is 1/4 . What is the probability of a tail followed by 2 heads on three flips of the coin?

Here is what I have so far: There are 2^3 possible outcomes {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, and only one way to get THH. I've hit a wall and any pointers would be appreciated.
• Feb 12th 2013, 03:41 AM
Plato
Re: Probability of a tail followed by 2 heads on a biased coin
Quote:

Originally Posted by battery88
Suppose we have a biased coin for which the probability of heads is 3/4 while the probability of tails is 1/4 . What is the probability of a tail followed by 2 heads on three flips of the coin?

If you were to look up the answer in the 'back-of-the-book' it would be:
$\frac{3}{2^6}$.

Now if you can explain to yourself WHY? or HOW? then you will understand.

HINT: $TTH$ is one out of eight which is a power of two.
• Feb 12th 2013, 12:01 PM
HallsofIvy
Re: Probability of a tail followed by 2 heads on a biased coin
Quote:

Originally Posted by battery88
Suppose we have a biased coin for which the probability of heads is 3/4 while the probability of tails is 1/4 . What is the probability of a tail followed by 2 heads on three flips of the coin?

Here is what I have so far: There are 2^3 possible outcomes {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, and only one way to get THH. I've hit a wall and any pointers would be appreciated.

The probability that the first coin is tails is 1/4. The probability that the second coin is heads 3/4. The probability that the third coin is heads is 3/4. The probability of three independent results, ABC, happening is P(A)P(B)P(C).