Probability and Expected Value

wc6h02

先黎條簡單既做開頭
What is the expected number of rolls of three dice before triple is first obtained?

P(triple)= 6*(1/6)^3 = 1/36
expected rolls = 1/P(triple) = 36

跟住類似既

A fair die is rolled repeatedly until the first time that 3 of the same number come up in a row. What is the expected number of rolls?

有一個假設
我諗到將 擲三次骰仔 當作做 擲一次
咁樣既情況下 其實同第一條差唔到
不過而家系計 expected number of rolls of one die

所以將  第一條既answer 乘 3
36*3 = 108 就系 第二條既answer

不過 其實個假設系有問題既
擲到 { 1 2 2 2 , 4 5 6 6 6, .....}都系其中一個possible outcome
而我個假設並唔包括呢個set裡面既outcome
所以我淨系估到 個 value 應該系 36 到 108 之間

最後呢條系我想計既

A fair die is rolled repeatedly until the first time that 3 of the same number appear. What is the expected number of rolls?

除左逐個遂個計,
有冇咩更好既方法去計?

14588563

暫時計到29/3

呢題數比較煩 好易計錯...所以我都係問下其他人先

你可以試下想想有咩case係要加1/2步

西藏之神

係咪M1黎?

A fair die is rolled repeatedly until the first time that 3 of the same number appear. What is the expected number of rolls?

可以用Geometric Distribution黎做..
P(X=x)=(1-p)^(x-1)p
E(x)=1/p

expected no. of rolled until the first time that 3 = 1/(1/6)^3 =216
唔知岩唔岩....