For a tyrannosaur with a taste for scientists:
(1)The number of scientists eaten has a binomial distribution with q=0.6 and
m=8.
(2)The number of calories of a scientist is uniformly distributed on
(7000,9000).
(3)The number of calories of scientists eaten are independent, and are
independent of the number of scientists eaten.
Calculate the probability that two or more scientists are eaten and exactly
two of those eaten have at least 8000 calories each.
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我的解答:
N:科學家數量
NC:卡路里大於8000的科學家數量
C:一名科學家的卡路里
C(8,2):C8取2
因為 N~bin(q=0.6,m=8) 及Pr(C>8000)=0.5
得到 NC~bin(q=0.6*0.5=0.3,m=8)
接著課本說答案是C(8,2)(0.3)^2(0.7)^6...........(a)
理由是如果有2位卡路里大於8000的科學家被吃,等於說至少有兩位科學家被吃
但我認為解答(a)式是卡路里大於8000的科學家中剛好有兩位被吃的機率
為什麼該機率剛好等於至少有兩位科學家被吃且剛好有兩位卡路里大於8000
謝謝回答
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