Question

What is the conditional probability that, when flipping a non-biased coin four times, there are at least two hs, given that the first flip is a h?

1. minhkhoi
The conditional probability that, when flipping a non-biased coin four times, there are at least two heads, given that the first flip is a head, is 3/4.
Calculating the Conditional Probability:
Let us assume that getting a head in the first flip of coin is event B
Also, let us assume that getting a head in on of the remaining three flips is A
Then we have to find the probability of A given B, that is, P(A|B).
The formula for conditional probability is given as follows,
P(A|B) = P (A∩B) / P(B)
The probability of getting two heads, P(A∩B) = 3/8
The probability of getting head in the first flip, P(B) = 1/2
∴ P(A|B) = (3/8) / (1/2)
P(A|B) = 3/4
Thus,  the conditional probability of getting at least two heads, given that the first flip is a head is 3/4.