A few weeks ago, I encountered the following question:
If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly twice in 3 consecutive flips ?
I figured this question using the formula
P=nCm*p^m*q^(n-m)
P=3C2*(1/2)^2*(1/2)^1=3/8=0.375
Then I saw another question similar to the one above asking the probability that the coin will land on head twice and tail once out of 3 flips.
I counted the outcomes to be 3/8, but the formula does not seem to work in this case.
So I am wondering what exactly is wrong w/ the formula or is there anything that has to be tweaked to make it work?
Your help is much appreciated!