p(A)= 13× 13 = 19。

So the probability that a family scores (5,3) is 19...(2 points).

(2) Event B: A family won a prize in the game.

Eligible scores include (5,3), (5,5), (3,5) * *.

So p (b) =13x13+13+13+03 =13.

So the probability of a family winning the prize is 13...(4 points)

(3) As can be seen from (2), the probability of winning the prize for each family is 13.

∴ x ~ b (413) ... (5 points)

P(X=0)=(23)4= 168 1，P(X = 1)= c 14( 13)(23)3 = 328 1，

p(X = 2)= C24( 13)2(23)2 = 248 1，

p(X = 3)= C34( 13)3(23)= 88 1，

P (x = 4) = (13) 4 =181,…( 10 point)

∴X distribution list is:

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