What???s the expected number of HH in 10 consecutive coin tosses ? ??? Quantitative Problems on Probability

First we will solve it using Recursion.

Let’s say E[n] = Expected number of HH in n consecutive tosses.
Say X[i] = Output ( H/T ) on the ith toss.

If first toss returns T, then expected number of HH in 10 tosses is same as expected number of HH inthe next 9 tosses.
E[10 | X[1] = T] = E[9].

If first toss returns H, then expected number of HH in 10 tosses is (1+E[9]) if 2nd toss returns H, and E[9] if 2nd toss returns T.

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