列表:
答错题数:0,1,2,3,4,5,6,7,8;
答错概率(计算结果比较长,你可以自己用计算机.这里给出简式)
0.7^8,8*0.3*0.7^7,28*0.3^2*0.7^6,
56*0.3^3*0.7^5,70*0.3^4*0.7^4,56*0.3^5*0.7^3,
28*0.3^6*0.7^2,8*0.3^7*0.7,0.3^8;
答错概率计算方法(0-8题,与答错题数一一对应):
设答错x题
说明:C(a,b)=b!/[(b-a)!*a!]
例:C(3,8)=8!/[(8-3)!*3!]=40320/(120*6)=56
(a!,b!:阶乘.例:6!=1*2*3*4*5*6)
答错概率通式为:C(x,8)*0.7^(8-x)*(1-0.7)^x
请注意先算次方,再算乘除
例:
答错0题,C(0,8)*0.7^8*0.3^0
答错3题,C(3,8)*0.7^5*0.3^3
答错8题,C(8,8)*0.7^0*0.3^8
设期望为E,
E= 0*0.7^8 + 1*8*0.3*0.7^7 + 2*28*0.3^2*0.7^6
+ 3*56*0.3^3*0.7^5 + 4*70*0.3^4*0.7^4 + 5*56*0.3^5*0.7^3
+ 6*28*0.3^6*0.7^2 + 7*8*0.3^7*0.7+8*0.3^8
E=2.4
所以答对题数的期望为2.4题