甲、乙两人进行定点投篮比赛,在距篮筐3米线内设一点,在点A处投

甲、乙两人进行定点投篮比赛,在距篮筐3米线内设一点,在点A处投中一球得2分,不中得0分;在距篮筐3米线外设一点B,在点B处投中一球得3分,不中得0.已知甲、乙两人在A点投中的概率都是,在B点投中的概率都是,且在AB两点处投中与否相互独立.设定甲、乙两人先在A处各投篮一次,然后在B处各投篮一次,总得分高者获胜.

I)求甲投篮总得分的分布列和数学期望;

II)求甲获胜的概率.

答案

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