Respuesta :
Answer:
The probability of obtaining exactly 5 correct answers on a ten question examination is 0.1366.
Step-by-step explanation:
Each multiple-choice questions has three options (a), (b) and (c).
The probability of getting a correct answer is, [tex]P(Correct)=\frac{1}{3}[/tex] since one of the three options is correct.
But this students has an unique way of selecting the answers.
He rolls a die and according to the result of the die he marks the answers.
The sample space of rolling a die is: S = {1, 2, 3, 4, 5, 6}
Odds of picking the three options are as follows:
- To pick (a): If 1 or 2 rolls of the die.
The probability to pick (a) is,
[tex]P (Selecting\ (a))=\frac{2}{6}=\frac{1}{3}[/tex]
- To pick (b): If 3 or 4 rolls of a die.
The probability to pick (a) is,
[tex]P (Selecting\ (b))=\frac{2}{6}=\frac{1}{3}[/tex]
- To pick (c): If 5 or 6 rolls of the die.
The probability to pick (a) is,
[tex]P (Selecting\ (c))=\frac{2}{6}=\frac{1}{3}[/tex]
Thus, all the three options have the equal probability of being picked.
Let X = Number of correct answers.
The number of questions is, n = 10 and probability of selecting a correct option is , p = [tex]\frac{1}{3}[/tex].
The random variable X follows Binomial distribution.
The probability function is:
[tex]P(X = x)={n\choose x}p^{x}(1-p)^{n-x}[/tex]
Compute the probability of obtaining exactly 5 correct answers on a ten question examination as:
[tex]P(X = 5)={10\choose 5}(\frac{1}{3} )^{5}(1-\frac{1}{3} )^{10-5}=0.1366[/tex]
Thus, the probability of obtaining exactly 5 correct answers on a ten question examination is 0.1366.
