Answer with Step-by-step explanation:
Part a)
Player A wins as follows:
1) He wins during the first toss itself.
2)Player A losses and then Player B also losses his turn and Player A wins subsequently
Probability of event 1 is 'p' (Given)
thus we have
[tex]P(A)=P(1)+P(2)\\\\P(A)=p+(1-p)^{2}\times P(A)\\\\\therefore P(A)=\frac{p}{1-(1-p)^{2}}=\frac{1}{2-p}[/tex]
Part b)
We have
[tex]P(A)=\frac{1}{2-p}[/tex]
Thus for least value put p = 0
Thus
[tex]P(A)>\frac{1}{2-0}\\\\\therefore P(A)>1/2[/tex]
