Can anyone help?? Two players, A and B, alternately and independently flip a coin and the first
player to obtain a head wins. Assume player A flips first and P(Head)=0.4. What is the probability that A wins?

Question

Can anyone help??  Two players, A and B, alternately and independently flip a coin and the first
player to obtain a head wins. Assume player A flips first and P(Head)=0.4. What is the probability that A wins?

turingtest · Answer

|dw:1423843565984:dw|$$P(\text{A wins})=P($$

turingtest · Answer

A wins if heads comes up on the first flip, or the third flip, or the fifth flip, or any odd flip$$P(A~wins)=P(H)+P(TTH)+P(TTTTH)+...$$which looking at the graph is$$P(A~wins)=0.4+0.6^2\cdot0.4+0.6^4\cdot0.4+...$$sum the series

anonymous · Answer

Thank you!  As soon as I saw your picture the sum of the series clicked.  
Much appreciated!!

turingtest · Answer

welcome!