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甲投篮命中率为0.8,乙投篮命中率为0.7,每人各投篮3次,求(1)甲命中1次且乙命中2次的概率;

来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/04/29 05:58:13
甲投篮命中率为0.8,乙投篮命中率为0.7,每人各投篮3次,求(1)甲命中1次且乙命中2次的概率;
(2)甲、乙命中次数相等的概率;(3)甲、乙两人共命中2次的概率?
甲投篮命中率为0.8,乙投篮命中率为0.7,每人各投篮3次,求(1)甲命中1次且乙命中2次的概率;
(1)P(甲命中1次)=3×0.8×0.2×0.2=0.096
P(乙命中2次)=3×0.7×0.7×0.3=0.441
所以P(A)=0.096×0.441=0.042336
(2)甲乙都一次没中:0.2×0.2×0.2×0.3×0.3×0.3=0.000216
甲乙都命中1次:3×0.8×0.2×0.2×3×0.7×0.3×0.3=0.018144
甲乙都命中2次:3×0.8×0.8×0.2×3×0.7×0.7×0.3=0.169344
甲乙都命中3次:0.8×0.8×0.8×0.7×0.7×0.7=0.175616
P(B)=0.000216+0.018144+0.169344+0.175616=0.36332
(3)甲0次乙2次:0.2×0.2×0.2×3×0.7×0.7×0.3=0.003528
甲1次乙1次:3×0.8×0.2×0.2×3×0.7×0.3×0.3=0.018144
甲2次乙0次:3×0.8×0.8×0.2×0.3×0.3×0.3=0.010368
P(C)=0.003528+0.018144+0.010368=0.03204