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)
Answer: 4 weeks and 5 days
Step-by-step explanation:
9 weeks = 63 days
63 + 2 = 65
4 weeks = 28 days
28 + 4 = 32
65 - 32 = 33
7 * 4 = 28
33 - 28 = 5
28 days = 4 weeks
Answer:
=375
Step-by-step explanation:
1500
4
=375
Answer:
C 37.5
Step-by-step explanation:
1 inch is 30 feet. so feet is 30 x [number of inches]. 30 x 1.25 = 37.5
Answer:
Step-by-step explanation:
If AE = EC, then E is the midpoint of AC.
If BF = FC, then F is the midpoint of BC.
That would mean that AB is parallel to EF.
Which would also mean that triangle ECF is similar to triangle ACB. So if angle EFC is 92, then angle DBF is 92 as well.
(Because we know that the length of EF is 10 and that EF is parallel to AB, then EF is half the measure of AB so AB = 20. Not really important here, but important to know. It's called the Triangle Midsegment Theorem.)
