I am stuck on a problem for my stats class. I have not done any work but I will explain why. Here is the problem;
- A coin is flipped until you get a tails. What is the probability of
getting at least 4 heads?
I have done probability with coins before, but this question stumped me. How? Because we only have ONE coin, and we don't know how many times the coin is tossed. I know that with one coin, the probability of getting a head is 1. And the number of outcomes is 2. However, I don't know the next step after this, especially when I'm not given information on how many times the coin should be tossed.
Any help would be great. Or maybe just a tip on looking at this problem from a different perspective? Thank you!
Best Answer
I've also started statistics as well.
How I look into this question is the other way around:
Rather than looking for 4 in a row, I look at the probability of not having 4 heads in a row (having the compliment of the probability).
Let say P(A) = Having at least 4 heads before first tail
$P(A') = P(T)+P(H\cap T)+P(H\cap H \cap T)+P(H \cap H \cap H \cap T)$
$P(A')+P(A) = 1 \rightarrow P(A) = 1-P(A') $
$1-P(T)+P(H\cap T)+P(H\cap H \cap T)+P(H \cap H \cap H \cap T)$
$ 1-[1/2 + 1/2^2 + 1/2^3 +1/2^4] = 1-15/16 = 1/16 $