Question

What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up heads?.

Answer 1

Answer:

Step-by-step explanation:

wow,  they really try to make these probablity questions difficult.  so they say 5 but really,  b/c the 1st one is heads ,  we are tossing the coin 4 more times, to find 3 heads b/c we already got one.    wow,  I'm mad at the teacher that asked this.  :P   Just say 4 flips for 3 heads.

P(H) = heads

P(H) =1/$2^{4}$   probability is 1/$2^{4}$ because we have two outcomes and four tries.

P(H) = 1/16

P(H>=3)  3 * 1/16

P(H>=3) = 3/16

if there is an argument that you have to take 1/$2^{5}$ into account by the teacher tell them that it was already resolved ,  the first flip is not a "probablity" any longer.  It's heads,  100%  ,  it doesn't affect the next tosses b/c this is a "fair" coin and it's going to land on heads  50% of the time, for every toss.   Just my rant.  :P