Question

求助一道条件概率的题目？

In the 2012 Summer Olympics, the head of the British drug testing said that the odds of the lab giving a positive result on a negative sample for an athlete was about 2 in 1000, or about 0.2%. Suppose that the tests are 95% accurate on positive samples (so they will all test positive), and that 10% of the athletes are actually using drugs. What is the conditional probability that an athlete who tested positive for drug use, actually had a positive sample?

Answer 1

由题意可知：

• 运动员实际服药概率：drug: P(D) = 10%；no drug: P(N) = 90%

• 检测的准确性：未服药检测为服药(position)的概率：P(P|N)= 0.2%；服药检测为服药(position)的概率：P(P|D)= 95%

• 问题: 检测结果为阳性，确实为阳性的概率P(D|P)？
  

• 解答：用公式可得：P(P) =P(P|N)*P(N) + P(P|D)*P(D)

  贝叶斯公式可得：P(D|P) = P(P|D)*P(D)/P(P)

  =P(P|D)*P(D)/(P(P|N)*P(N) + P(P|D)*P(D))

  =95*10/(0.2*90 + 95*10)

  =0.981405

看下对不。稍微改一下。。。你懂的。。

Answer 2

获得优秀的条件是：答对5道及以上.分步骤计算更容易理解.1、答对5道题5道题肯定从会的10道中选,选法：C(10,5)还有1道没答对,选法：C(10,1)答对五道的选法：C(10,5)*C(10,1)=25202、答对6道题6道题全部答对,选法：C(10,6)答对6道题选法：C(10,6)=2103、答对4道题4道题肯定从会的10道中选,选法：C(10,4)还有2道没答对,选法：C(10,2)答对4道题选法：C(10,4)/C(10,2)=9450过关的选法：2520+210+9450=12180优秀概率：(2520+210)/12180=0.2241

Answer 3

等品概率应：70%*90%+30%*80%=87%
问应该（70%*90%）（甲等品）除（70%*90%+30%*80%）=63/87

Answer 4

A --- 校概率 设：P(A)=1/3.
B --- 刘畅校概率 设： P(B)=1/3.
假刘畅朋友同班同则刘畅独立
P(B|A) 校情况校概率概率应接近1.

假李雷认识同班同则李雷独立
C --- 李雷校概率 设： P(C)=1/3.
P(C|A) 校情况李雷校概率概率应接近1/3说校影响李雷校

Answer 5

哈哈哈，阁下是复旦研究生吧，感受来自生物信息学的怒视