Question

A coin is biased so that the probability of the coin landing heads is 2/3. This coin is tossed three times. A) Find the probability that it lands on heads all three times. B) Use answer from part (A) to help find the probability that it lands on tails at least once.

Answer 1

The tossing of the biased coin can be thought of as a series of bernoullian trials and each trial follows a bernoulli distribution.

So, the probability of getting a head=2/3=p

let X denote the number of heads in the 3 trials.

X ~ Bin(3,p)

A) Probability that it lands on heads all three times = P[X=3] =

B) Probability that it lands on tails at least once= 1 - probability of no tail in the 3 trials

= 1 - Probability that it lands on heads all three times