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 :[tex]\frac{5}{10}=\frac{1}{2}[/tex]
q is the probability of the false answers which is :[tex]1-p=1-\frac{1}{2}=\frac{1}{2}[/tex]
We will use the model by substituting the values we get:
[tex]P(x)=[\frac{n!}{x!(n-x)!}]p^xq^{n-x}[/tex] on substituting the values we get:
[tex]P(x)=[\frac{`10!}{5!(5)!}]\frac({1}{2})^5\cdot \frac{1}{2}^{5}[/tex]
[tex]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[/tex]
Cancel out the common terms from numerator and denominator we get:
[tex]\frac{10\cdot9\cdot8\cdot7\cdot6}{5\cdot4\cdot3\cdot2}\frac{1}{32}\cdot\frac{1}{32}[/tex]
[tex]\Rightarrow 14\cdot18\cdot\frac{1}{1024}[/tex]
[tex]\Rightarrow \frac{14\cdot18}{1024}[/tex]
[tex]\Rightarrow \frac{252}{1024}[/tex]
[tex]\Rightarrow 0.2460[/tex]
