甲乙二人投篮,命中率分别是0.7和0.6,每人投三次,求甲比乙进球数多的概率

题目

甲乙二人投篮,命中率分别是0.7和0.6,每人投三次,求甲比乙进球数多的概率

答案

甲进球比乙多,有以下情况
1,1：0
C(3.1) 0.7X0.3X0.3X0.4X0.4X0.4=0.012
2 2:0
C(3.2)0.7X0.7X0.3X0.4X0.4X0.4=0.028
3 2:1
C(3.2)0.7X0.7X0.3XC(3.1)0.6X0.4X0.4=0.127
4 3:0
0.7X0.7X0.7X0.4X0.4X0.4=0.022
5 3:1
0.7X0.7X0.7XC(3.1)0.6X0.4X0.4=0.099
6 3:2
0.7X0.7X0.7XC(3.2)0.6X0.6X0.4=0.148
P=0.012+0.028+0.127+0.022+0.099+0.148=0.436 =43.6%