Scando-Germanic friend, Odd Zahlen, often brings a die to class to answer multiple-choice final exam questions. Each multiple-choice question on this particular examination consists of three choices, and Odd decides to pick answer (a) if a 1 or 2 appears on a roll of the die, to pick (b) if a 3 or 4 appears on the die, or to pick (c) if a 5 or 6 appears. Assume that the correct answers are uniformly distributed among the choices (a), (b), and (c). What is the probability of obtaining exactly 5 correct answers on a ten question examination using this method?

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:

        The probability to pick (a) is,

        The probability to pick (a) is,

        The probability to pick (a) is,

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 = .

The random variable X 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.