Question

Answer part a and part b please!!!

(a) What is the conditional probability that exactly four Tails appear w when a fair coin is flipped six times, given that the first flip came up Heads? (I.e. the coin , then is flipped five more times with Tails appearing exactly lour times.) (b) What if the coin is biased so that the probability of landing Heads is 1/3? (Hint: The binomial distribution might be helpful here.)

Answer 1

a) It is given that the first flip is heads, so we can get exactly 4 tails in the next five flips as follows:

5C4*1/2^5 = 0.3125

b) If the coin is biased, here Probability of getting a tail = 1-1/3 = 2/3

Since the first flip is a head, probability of getting exactly 4 tails in the next 5 flips: 5C4*(2/3)^4*(1/3) = 0.3292