Traveling for four people, there are two places to choose from, A and B, but they don't know where to play, so they decide to throw a unified one.

(1) According to the meaning of the question, the probability of each of these four people going to A is 13.

The probability of going to B is 23.

Suppose that "just one of these four people goes to A" is the event AI (I = 0, 1, 2, 3, 4).

∴P(Ai)=Ci4( 13)i(23)4？ I (2 points)

The probability that these four people just 1 go to a place to play games is p (a1) = c14 (13)1(23) 3 = 3281. (4 points).

(2) Let "the number of people going to place A is greater than the number of people going to place B" as event B, then B=A3∪A4,

∴ p (b) = p (a3)+p (a4) = 19。 (8 points)

(3) All possible values of ξ are 0, 3, 4,

P(ξ= 0)= P(A0)+P(A4)= 168 1+ 18 1 = 178 1，

P(ξ= 3)= P(a 1)+P(A3)= 328 1+88 1 = 408 1，

P (ξ = 4) = P (A2) = 248 1，( 10)

The ∴ξdistribution list is

ξ034 p 178 1408 1248 1eξ= 0× 178 1+3×408 1+4×248 1 =