Coin toss probability question

[Win_odd Dhamnekar]

How to find the probability that a person tossing three coins will get either all heads or all tails for the second time on the fifth toss.

Answer. I don't have any idea to solve this question. In a single toss of three coins, a probability that a person will get either all heads or tails is 0.25.

 

[Romsek]

\(\displaystyle
\text{let $A$ be the event of getting all heads or tails}\\
\text{you want the probability of $A$ occuring only once in tosses 1-4 and then again on toss 5}\\
\text{This probability is given by } \\
\dbinom{4}{1}P[A] (1-P[A])^3 \cdot P[A] = 4 \cdot \dfrac 1 4 \cdot \left(\dfrac 3 4\right)^3 \cdot \dfrac 1 4 = \dfrac{27}{256}
\)