Ask Question
7 April, 01:04

A fair coin is tossed n times. What is the probability that no two consecutive heads appear? A fair coin is tossed n times. What is the probability that no two consecutive heads appear?

+1
Answers (1)
  1. 7 April, 02:35
    0
    If a coin is tossed, for example, 10 times:

    There are 2^10 = 1024 total possible outcomes of 10 tosses.

    Now we count the number of possible outcomes with no two consecutive heads. Let x_n be this number for n tosses - we wish to find x_10. For n > 2, the string of tosses must fall into one of two disjoint categories:

    (i) tosses ending with a tail

    (ii) tosses ending with a tail then a head

    (i. e. tosses ending with a head then a head is impossible)

    Given that the first n-1 or n-2 tosses must also have no two consecutive heads, we sum the number of possibilities of case (i) and (ii) and find

    x_n = x_{n-1} + x_{n-2}.

    We also easily see that x_1 = 2, x_2 = 3. From the above recurrence we can compute x_n as terms of the Fibonacci sequence until x_10 = 144.

    Since the coin is unbiased all these possibilities are equally likely and the answer is 144/1024 = 9/64.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A fair coin is tossed n times. What is the probability that no two consecutive heads appear? A fair coin is tossed n times. What is the ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers