(1)甲和乙之间进行三场比赛,甲恰好胜两场的概率为P=×0.62×0.4=0.432. (2)记“甲胜乙”,“甲胜丙”,“甲胜丁”三个事件分别为A,B,C,则P(A)=0.6,P(B)=0.8,P(C)=0.9. 则四名运动员每两人之间进行一场比赛,甲恰好胜两场的概率为 P(AB+AC+BC) =P(A)P(B)[1-P(C)]+P(A)[1-P(B)]P(C)+[1-P(A)]P(B)P(C) =0.6×0.8×0.1+0.6×0.2×0.9+0.4×0.8×0.9 =0.444. (3)随机变量的可能取值为0,1,2,3. 的 P(=0)=0.4×0.2×0.1=0.008; P(=1)=0.6×0.2×0.1+0.4×0.8×0.1+0.4×0.2×0.9=0.116; 由(2)得P(=2)=0.444; P(=3)=0.6×0.8×0.9=0.432. ∴随机变量的概率分布为
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| 0.008
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