甲乙两人投篮,投中的概率分别为0.6、0.7.现各投3次,求两人投中次数相等的概率。

2025-02-22 12:56:20
推荐回答(2个)
回答1:

分四种情况,
一 都进0球
二 都进一球
三 都进两球
四 都进三球
四种情况分别算的概率相加

甲:0中概率 0.4*0.4*0.4 =0.064
1中概率 0.4*0.6*0.4*3=0.288
2中概率 0.4*0.6*0.6*3=0.432
3中概率 0.6*0.6*0.6 =0.216
乙:0中概率 0.3*0.3*0.3 =0.027
1中概率 0.7*0.3*0.3*3=0.189
2中概率 0.7*0.7*0.3*3=0.441
3中概率 0.7*0.7*0.7 =0.343

故两人投中相等的概率是:
0.064*0.027+0.288*0.189+0.432*0.441+0.216*0.343=0.001728+0.054432+0.074088=
0.130248

回答2:

1.两人都投中1次:3*0.6*0.4*0.4*3*0.7*0.3*0.3

两人都投中2次:3*0.6*0.6*0.4*3*0.7*0.3*0.7

两人都投中3次:0.6*0.6*0.6*0.7*0.7*0.7

两人投中次数相等的概率=3*0.6*0.4*0.4*3*0.7*0.3*0.3+3*0.6*0.6*0.4*3*0.7*0.3*0.7+0.6*0.6*0.6*0.7*0.7*0.7

甲2乙1:3*0.6*0.6*0.4*3*0.7*0.3*0.3

甲3乙2:0.6*0.6*0.6*3*0.3*0.7*0.7

甲比乙投中次数多=3*0.6*0.6*0.4*3*0.7*0.3*0.3+0.6*0.6*0.6*3*0.3*0.7*0.7