not letting me add answer
Refer to the attachment
Answer:
1, 13
-1, -13
here are 2 coefficient factors that multipy to get 13
brain list please?
Answer:
![P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}](https://tex.z-dn.net/?f=P%28C%3D1%7CT%3D1%29%3Dq%28%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%20p%5Ei%281-p%29%5E%7B20-i%7D%29%28%20%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%5Bqp%5Ei%281-p%29%5E%7B20-i%7D%20%2B%20%281-q%29p%5E%7B20-i%7D%281-p%29%5Ei%5D%29%5E%7B-1%7D)
Step-by-step explanation:
Hi!
Lets define:
C = 1 if candidate is qualified
C = 0 if candidate is not qualified
A = 1 correct answer
A = 0 wrong answer
T = 1 test passed
T = 0 test failed
We know that:

The test consist of 20 questions. The answers are indpendent, then the number of correct answers X has a binomial distribution (conditional on the candidate qualification):

The probability of at least 15 (P(T=1))correct answers is:

We need to calculate the conditional probabiliy P(C=1 |T=1). We use Bayes theorem:

![P(T=1)=q\sum_{i=15}^{20}f_1(i) + (1-q)\sum_{i=15}^{20}f_0(i)\\P(T=1)=\sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i)]](https://tex.z-dn.net/?f=P%28T%3D1%29%3Dq%5Csum_%7Bi%3D15%7D%5E%7B20%7Df_1%28i%29%20%2B%20%281-q%29%5Csum_%7Bi%3D15%7D%5E%7B20%7Df_0%28i%29%5C%5CP%28T%3D1%29%3D%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%5Bqp%5Ei%281-p%29%5E%7B20-i%7D%20%2B%20%281-q%29p%5E%7B20-i%7D%281-p%29%5Ei%29%5D)
![P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}](https://tex.z-dn.net/?f=P%28C%3D1%7CT%3D1%29%3Dq%28%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%20p%5Ei%281-p%29%5E%7B20-i%7D%29%28%20%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%5Bqp%5Ei%281-p%29%5E%7B20-i%7D%20%2B%20%281-q%29p%5E%7B20-i%7D%281-p%29%5Ei%5D%29%5E%7B-1%7D)