Answer:
0.2461
Step-by-step explanation:
The binomial distribution model formula is
[tex]P(x)=[\frac{n!}{x!(n-x)!}]p^{x}q^{n-x}[/tex]
Where
- P(x) is the probability
- n is the is total number of questions (here n = 10)
- x is the the number of questions we are looking for (we are looking for 5 out of 10 to be right, so x = 5)
- p is the probability of success (here we want 5 questions right, so probability of being right in true of false question is [tex]\frac{1}{2}[/tex])
- q is the probability of failure (here it means getting the answer wrong, so probability of wrong is [tex]\frac{1}{2}[/tex])
Now, we plug-in all the info into the formula and figure out the "probability that the student gets 5 out of 10 questions right":
[tex]P(x)=[\frac{n!}{x!(n-x)!}]p^{x}q^{n-x}\\P(x)=[\frac{10!}{5!(10-5)!}](\frac{1}{2})^{5}(\frac{1}{2})^{10-5}\\P(x)=[\frac{10!}{5!5!}](\frac{1}{2})^{5}(\frac{1}{2})^{5}\\P(x)=[252](\frac{1}{2})^{10}\\P(x)=0.2461[/tex]
