### Instruction: A fair coin is tossed six times and the sequence of heads and tails is recorded. What is the probability that the sequence contains exactly two heads? Express your answer as a common fraction.### Response: To find the probability of an event, I need to divide the number of favorable outcomes by the number of possible outcomes.
In this case, the possible outcomes are all the sequences of heads and tails that can occur when tossing a coin six times.
There are 2^6 = 64 such sequences, since each toss has two choices and they are independent.
The favorable outcomes are those sequences that contain exactly two heads.
I can think of this as choosing two positions out of six for the heads to appear, and the rest will be tails.
The number of ways to choose two positions out of six is 6 choose 2, which is 6! / (2! 4!) = 15.
So there are 15 favorable outcomes out of 64 possible outcomes.
Therefore, the probability is 15/64.