1/4 is the answer to the problem
Answer:
0.2460 is the required probability.
Step-by-step explanation:
We have been given binomial model
n is the total number of questions which is 10
x is the questions taken out to be which is 5
p is the probability of right answers which is :![\frac{5}{10}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D)
q is the probability of the false answers which is :![1-p=1-\frac{1}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=1-p%3D1-%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
We will use the model by substituting the values we get:
on substituting the values we get:
![P(x)=[\frac{`10!}{5!(5)!}]\frac({1}{2})^5\cdot \frac{1}{2}^{5}](https://tex.z-dn.net/?f=P%28x%29%3D%5B%5Cfrac%7B%6010%21%7D%7B5%21%285%29%21%7D%5D%5Cfrac%28%7B1%7D%7B2%7D%29%5E5%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5E%7B5%7D)
![P(x)=\frac{10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!(5\cdot4\cdot3\cdot2\cdot1)}\cdot\frac{1}{2}^5\cdot\frac{1}{2}^5](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B10%5Ccdot9%5Ccdot8%5Ccdot7%5Ccdot6%5Ccdot5%21%7D%7B5%21%285%5Ccdot4%5Ccdot3%5Ccdot2%5Ccdot1%29%7D%5Ccdot%5Cfrac%7B1%7D%7B2%7D%5E5%5Ccdot%5Cfrac%7B1%7D%7B2%7D%5E5)
Cancel out the common terms from numerator and denominator we get:
![\frac{10\cdot9\cdot8\cdot7\cdot6}{5\cdot4\cdot3\cdot2}\frac{1}{32}\cdot\frac{1}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Ccdot9%5Ccdot8%5Ccdot7%5Ccdot6%7D%7B5%5Ccdot4%5Ccdot3%5Ccdot2%7D%5Cfrac%7B1%7D%7B32%7D%5Ccdot%5Cfrac%7B1%7D%7B32%7D)
![\Rightarrow 14\cdot18\cdot\frac{1}{1024}](https://tex.z-dn.net/?f=%5CRightarrow%2014%5Ccdot18%5Ccdot%5Cfrac%7B1%7D%7B1024%7D)
![\Rightarrow \frac{14\cdot18}{1024}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B14%5Ccdot18%7D%7B1024%7D)
![\Rightarrow \frac{252}{1024}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B252%7D%7B1024%7D)
![\Rightarrow 0.2460](https://tex.z-dn.net/?f=%5CRightarrow%200.2460)
I’m not so sure about this one but my guess would be maybe C
First, find out c
4c=-12, so c=-3
-5c=d, so d=15