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, 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,
- To pick (b): If 3 or 4 rolls of a die.
The probability to pick (a) is,
- To pick (c): If 5 or 6 rolls of the die.
The probability to pick (a) is,
Thus, all the three options have the equal probability of being picked.
Let <em>X</em> = Number of correct answers.
The number of questions is, <em>n</em> = 10 and probability of selecting a correct option is , p = .
The random variable <em>X</em> follows Binomial distribution.
The probability function is:
Compute the probability of obtaining exactly 5 correct answers on a ten question examination as:
Thus, the probability of obtaining exactly 5 correct answers on a ten question examination is 0.1366.