[問題] 一題機率的問題？

[check (且可)]

從高中畢業後就沒有讀相關機率的科目了
想不到中山資管沒考統計的那組，在某些考科也有一些機率的問題

97中山資管-資料結構
Suppose you have three coins, A, B,and C.
A is a fair coin, B has 3/4 probability of coming up with head,
and C always comes up with head.

(A)If you choose B and toss it three times,what is the probability
that you get three heads?

(B)If you randomly choose a coin, toss it three times,
and get three heads,what is the probability that the coin you
chose is C?

請問(A)是(3/4)*(3/4)*(3/4)嗎？
(B)就不知道要怎麼解了？
麻煩幫忙一下，非常感謝。

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推 BF3716:(A) 算法是正確的
→ BF3716:(B) 有1/3會抽到A銅板，此時連三正面=(0.5)*(0.5)*(0.5)
→ BF3716:    有1/3會抽到B銅板，此時連三正面=(0.75)*(0.75)*(0.75)
→ BF3716:    有1/3會抽到C銅板，此時連三正面=(1)*(1)*(1)
→ BF3716:總共機率為 (1/3)*(1/8)+(1/3)*(27/64)+(1/3)*1
推 BF3716:抽到C銅板的機率為 (1/3)*1*1*1/總共機率
推 zegolas:謝謝BF大的解答。
→ check:非常感謝BF大的回應，祝您考上理想的學校。