A fair coin is tossed repeatedly. The probability of getting a result in fifth toss different from those obtained in the first then four tosses is

$\frac{1}{16}$

Let $H_i$ denote the event of getting a head in $i^{th}$ and $T_¡$ denote the event of getting a tail in $i^{th}$ toss. Then,

Required probability 

$=P\begin{Bmatrix}(H_1∩ H_2∩ H_3 ∩H_4∩ T_5)∪ (T_1∩ T_2∩ T_3∩ T_4∩H_5)\end{Bmatrix}$

$=P(H_1∩ H_2∩ H_3 ∩H_4∩ T_5)+P (T_1∩ T_2∩ T_3∩ T_4∩H_5)$

$= P(H_1)P(H_2)P(H_3)P(H_4)P(T_5)+P(T_1)P(T_2)P(T_3)P(T_4)P(H_5)$

$=\left(\frac{1}{2}\right)^5+\left(\frac{1}{2}\right)^5=\frac{1}{16}$