Question

My 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?

Answer 1

`P(A=5)= 0.1366`

Explanation:

From each multiple-choice question, there consists three answers to each;

So the probability of picking, the correct answer as they are uniformly distributed among the choices (a), (b), and (c) will be;

P(correct answer) =
`(1)/(3)`

Now, to determine the probability of obtaining exactly 5 correct answers on a ten question examination using this method

Let use A as representative for the numbers of correct answers out of 10 questions that is being answered.

∴

`P(A=5)= [\left \ {{10} \atop {5}} \right.]`
`((1)/(3)) ^5`
`(1-(1)/(3))^(10-5)`

`P(A=5)= [\left \ {{10} \atop {5}} \right.]((1)/(3)) ^5 ((2)/(3)) ^5`

`P(A=5)= 0.13657`

`P(A=5)= 0.1366`