perfect asked in 社會與文化語言 · 1 decade ago

統計學的問題(麻煩給我詳解~!!謝謝)

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

Update:

麻煩給我詳解和說明~~感謝!!!!!!

Update 2:

抱歉~不是要中文翻譯喔^^

2 Answers

Rating
  • 1 decade ago
    Favorite Answer

    (1) P(head)=0.5

    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) > 1/2

    Source(s): Introduction to probability
  • 1 decade ago

    2遊戲者和B交替和獨立地擲硬幣和第1名演員獲得頭勝投. 猜想遊戲者拋首先.

    (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

    希望這些對你有幫助。

    Source(s): 自己
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