Question

Six persons throw for a stake, which is to be won by the one who first throws head with a penny; if they throw in succession, find the chance of the fourth person.

Answer 1

Probability for all six person to win$=\frac{1}{2}$
Probability for fourth person to win if he throws head with penny is
$\Rightarrow$Let person win denoted by $A,B,C,D,E,F$
Person loss$\Rightarrow A^{{}^{\prime }},B^{{}^{\prime }},C^{{}^{\prime }},D^{{}^{\prime }},E^{{}^{\prime }},F^{{}^{\prime }}$
For $4^{th}$ or $D$ to win$\Rightarrow A^{{}^{\prime }}{B}^{{}^{\prime }}{C}^{{}^{\prime }}D$
$\Rightarrow \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$
$\Rightarrow \frac{1}{2^4}$