Consider the experiment in which a person flips a loaded coi

Consider the experiment in which a person flips a loaded coin such that head is three times more likely to appears than tail. Suppose that the coin is flipped 3 times. (a) List all the outcomes of this experiment and their respective probabilities. (b) What is the probability of getting at least one tail in this experiment? (c) Given that the first two tosses were head, what is the probability of getting another head in the third tos

Solution

Probability of head = 3/4 ; Probability of tail = 1/4

a) outcomes = { HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}

B) ATLEAST ONE TAIL ={HHT,HTH,THH,HTT,THT,TTH,TTT}

Prob(at least one tail ) = 1-Prob(HHH)=1-(27/64)= 0.578125

c)Given that the first two tosses were head, the probability of getting another head in the third toss = Prob (head) = 3/4

Since the tosses are independent.