What is the probability that two Heads do not occur consecutively when a fair coin is tossed 10 times?
Answers
Step-by-step explanation:
Possible number of patterns (total number of combinations) 2^n (each time either H or T=2 outcomes, 10 times=2^10).
Let's check two consecutive H:
If we toss once we'll have 2^1=2 combinations: H, T - 2 outcomes with NO 2 consecutive H.
If we toss twice we'll have 2^2=4 combinations: HT, TH, TT, HH - 3 outcomes with NO 2 consecutive H.
If we toss 3 times we'll have 2^3=8 combinations: TTT, TTH, THT, HTT, HTH, HHT, THH, HHH 5 outcomes with NO 2 consecutive H.
If we toss 4 times we'll have 2^4=16 combinations:... 8 outcomes with NO 2 consecutive H.
...
On this stage we can see the pattern in "no consecutive H": 2, 3, 5, 8...
I guess it's Fibonacci type of sequence and it will continue: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
144 is outcomes with no consecutive H if we toss 10 times.