Question

Amanda, Becky, and Charise toss a coin in sequence until one person “wins” by tossing the first head. a) If the coin is fair, find the probability that Amanda wins. b) If the coin is fair, find the probability that Becky wins. c) If the coin is not necessarily fair, but has a probability p of coming up heads, find an expression involving p for the probability that Becky wins. d) As in part c) find similar expressions for Amanda and Charise and plot all three for 0<p<1

Answer 1

Since coin is tossing in sequence Amanda toss a coin first

She has half probability of loss and half probability of win on very first toss.

Probability of Amanda ins=1/2

P(Becky wins|Amanda loose)=p(loosing Amanda).p(Becky wins)/p(Amnada loose)

                       = (1/2*1/2) / 1/2=1/2

Now probability of winning=p

loosing=1-p

P(Becky wins|Amanda loose)=p(loosing Amanda).p(Becky wins)/p(Amnada loose)

                                            = (1-p)*p/1-p=p

P(Amanda wins)=p

P(Charies wins|Becky loose)= p