Question

概率论求解

题目：一种新方法对某种特定疾病的诊断准确率是95%，人群的发病率是0.005。（1）甲在身体普查中被判断患病，甲的确患病的概率是多少？（2)甲再次复查又被判断有病时，甲的确患病的概率是多少？（3）甲在第三次复查中又被判断有病，甲的确患病的概率是多少？

Answer 1

反复运用全概率公式
1)
Pall = 0.005 * 95/100 + 0.995 *5/100 =5450/100000
Pyes=0.005*95/100 = 475/100000
P1 = Pyes/Pall = 475 / 5450=19/218 =!= 8.716%

2)
Pall = 0.005 * 95/100 * 95/100 + 0.995 * 5/100 * 5/100 = 70000/10000000
Pyes = 0.005 * 95/100 * 95 /100 =45125/10000000
P2 = Pyes/Pall = 45125/70000=361/560 =!= 64.464%

3)
Pall = 0.005 * (95/100)^3 + 0.995 *(5/100)^3 = 4411250/1000000000
Pyes = 0.005 * (95/100)^3 = 4296875/1000000000
P3 = Pyes / Pall = 4296875/4411250 = 6875/7058 =!= 97.407%