Two players A and B alternately and independently flip a coin and the first player to obtain a head wins. Assume player A flip first.
(1)Is the coin is fair , what is the probability that. A wins?
(2)Show that for all p, 0<p<1 , where p= P(head) ,P(A wins)>1/2
- 1 decade agoFavorite Answer
let E denotes the event that first fliper to win.
=> P(E)=0.5+ (1-0.5)^2 * P(E)
=> P(E) = 0.5/0.75 = 2/3
(2) Formula is the same , just replace 0.5 with p , we get
P(E)=p + (1-p)^2 * P(E) , solve P(E)
=> P(E) = 1 / (2-p) , since 0<1<p
P(E) > 1/2Source(s): Introduction to probability
- 1 decade ago
(1)硬幣是美麗的 , 什麼是可能性那個. 勝投?
(2儘管p,的)Show <p<1 , 在哪裡p= P (頭) ,P (勝投)>1/2