Consider an experiment in which you flip four fair coins. Identify the possible outcomes of this experiment. Calculate the conditional probability that all four flips will be heads. Then calculate the conditional probability of flipping four heads, given that the first two flips were heads. Use a tree diagram to illustrate all of the possible outcomes, and complete the probability for each branch of the tree.
Now assign a random variable x, where the value of x is equal to the number of heads observed in the flips. Describe the probability distribution of x, and calculate the probability of observing three heads in four coin flips.