A fair coin and a biased coin where the probability of obtaining a head is twice the probability of obtaining a tail. if both are tossed simultaneously, find the probability that they are:

a) both heads

b) both tails

c) one head

d) at least one head

See below in bold.

Step-by-step explanation:

For the fair coin Prob (head) = 1/2 and Prob (Tail) = 1/2.

For the biased coin it is Prob (head) = 2/3 and Prob (Tail) = 1/3.

a) Prob (2 heads) = 1/2 * 2/3 = 1/3.

b) Prob (2 tails) = 1/2 * 1/3 = 1/6.

c) Prob (1 head) = Prob (H T or T H) = 1/2 * 1/3 + 1/2 * 2/3) = 1/6+1/3 = 1/2.

d) Prob (at least one head) = prob (HH or TH or HT) = 1/3 + 1/2 = 5/6.