Question

If in an experiment of tossing of a fair coin 10 times, probability when no two heads are consecutive is p, then find the value of 64 p. 

Answer 1

Let a_n denotes the number of outcomes in which no two consecutive head occurs in n tosses clearly a₁ = 2 and a₂ = 3. Let us consider last outcome is fixed as tail then we cannot have two consecutive heads in first (n – 1) tosses in a_n−1 ways and if last outcome is head we must have tail at (n – 1)^th toss and cannot have two consecutive heads in first (n – 2) tosses in a_n−2 ways. So,