We have a fair coin: tails and heads have the same probability (p=0.5).
We have to calculate which event has a greater probability:
O Two heads
O All three options have the same probability
O Two tails
O One head and One Tail
We can make a 2-steps tree diagram for the coin toss:
Two heads (HH) has a probability of 0.25.
Two tails (TT) has the same probability of 0.25.
One head and one tail can be reached getting tail or head first, so it has two ways of arriving to that result: HT and TH, so it has a probability of 2*0.25=0.5.
Answer: One head and one tail has a greater probability (p=0.5).