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A mathematical random variable problem
(1) Because everyone has five choices, there are 5*5*5= 125 possibilities according to step-by-step multiplication.

(2) If it is difficult, first calculate the probability of three people working in different societies.

N (ω) = 125n (different clubs) =5*4*3=60 p (different clubs) =60/ 125= 12/25.

So the probability that at least two of the three people join the same club is1-12/25 =13/25.

(3)x conforms to the binomial distribution p(x=i)=(C above I below 3) * ((kloc-0//5) I) * ((4/5) (3-I)).

x 0 1 2 3

p 64/ 125 48/ 125 12/ 125 1/ 125

e(x)=(64/ 125)* 0+(48/ 125)* 1+( 12/ 125)* 2+( 1/ 125)* 3 = 3/5