I flip a fair coin independently 6 times resulting in a sequ

I flip a fair coin, independently, 6 times, resulting in a sequence of heads (H) and tails (T). For each (consecutive) HTH in this sequence, you win $5. Define the random variable X to be the amount of dollars that you win. For example, if the sequence is THTHTH, then X = 10. What is the expected value of X? (a) 2/5 (b)2 (c) 5/2

Solution

c. 5/2