Can someone help me with this one?
A fair coin is tossed 5 times, what is the probability of a sequence of 3 heads? I can see that there are 2*2*2*2*2 possible outcomes, but how many of these include 3 heads in a sequence and why?
Total number of possible events = 2^5 = 32
Frequency of exactly 3 heads (HHHT*, THHHT, *THHH) = 2+1+2 = 5
Frequency of exactly four consecutive heads (HHHHT, THHHH) = 2
Frequency of five consecutive heads = 1
Frequency of required events = 5+2+1 = 8
Required probability = 8/32 = 1/4