Afair 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.