1. The problem statement, all variables and given/known data Suppose you will toss a coin 10 times. A) Compute the probability of event A that the longest run of consecutive Heads has length 5 (i.e., within your 10 tosses there is a run of 5 Heads in a row, but not 6 consecutive Heads.) B) Compute the probability of the event B that the longest run of consecutive Heads has length 5 or more. 2. Relevant equations Basic permutations, combinations, and counting rules. 3. The attempt at a solution Okay, so, I am pretty sure I have solved this in a very long and cumbersome way. There has to be a simpler way to do it. My approach: I essentially counted the "possible" outcomes. For instance, one example that satisfies P(A) = H,H,H,H,H,T,2,2,2,2. Thus, there are 24 possible outcomes for that specific sequence/position that satisfies A. I continued from there, moving to the right, placing a "T" before and after my sequence of 5 consecutive heads to act as a placeholder allowing me to compute the number of ways such a sequence, at such a position, could occur. I did a similar approach for B. Suprisingly enough, my results were a probability of.0625 for both of them. My question is this: Is there a better way than to sit there and try to chart out the possible placements and outcomes? What makes this hard is the consecutive placement. I have taken Calculus I, Calculus II, and various other math classes below it, however, this is my first serious "Probability" class. Thanks in advance for any help.