Answer:
0.140625
Explanation:
Total numbers of possible combinations for a coin = 2^n
If the coin is tossed 10 times, we have 2^10 = 1024
If the coin is tossed once, we have 2^1 = 2 outcomes.
The possible outcomes are H, T.
We have 2 outcomes with no two consecutive head.
If the coin is tossed twice, we have 2^2 = 4 outcomes.
The possible outcomes are HH, HT, TH, TT
We have 1 outcome with two consecutive heads and 3 outcomes without two consecutive heads.
If the coin is tossed thrice, we have 2^3 = 8 outcomes.
The possible outcomes are HHH, HHT, HTH, HTT, TTH, THT, THH and TTT
We have 3 outcomes with two consecutive head and 5 outcomes without two consecutive heads.
Comparing the results from the outcomes of the coin,we have 2,3,5,......
This looks like a financial sequence. For the next 10 tosses, we have
2,3,5,8,13,21,34,55,89,144
We have 144 outcomes without two consecutive heads if the coin is tossed 10 times
Pr(number of two consecutive Heads in 10 tosses) = 144/1024
= 0.140625