Respuesta :
Answer:
The required probability is [tex]\frac{11}{243}[/tex].
Step-by-step explanation:
Consider the provided information.
On a multiple-choice exam with three possible answers for each of the five questions.
That means the Probability of guess being correct is = [tex]p=\frac{1}{3}[/tex]
The Probability of guess being incorrect is = [tex]q=\frac{2}{3}[/tex]
We need to find the probability that a student would get four or more correct answers just by guessing.
Let X represents the probability of being correct
[tex]P(X\geq4)=P(X=4)+P(X=5)[/tex]
Use the binomial distribution: [tex]^nC_r=\binom{n}{r}p^rq^{n-r}[/tex]
[tex]P(X\geq4)=\binom{5}{4}(\frac{1}{3})^4(\frac{2}{3})^{1}+\binom{5}{5}(\frac{1}{3})^5(\frac{2}{3})^{0}[/tex]
[tex]P(X\geq4)=5\times(\frac{1}{3})^4(\frac{2}{3})^{1}+(\frac{1}{3})^5\\\\P(X\geq4)=\frac{10}{243}+\frac{1}{243}\\\\P(X\geq4)=\frac{11}{243}[/tex]
Hence, the required probability is [tex]\frac{11}{243}[/tex].
