Question

1) A multiple choice test consist of 6 questions with 3 possible answers for each (only 1 or which is correct). A student decides to roll dice to help them out. They have decided that if they roll a 1 or a 2, they will select the first answer, a 3 or a 4- the second answer, and 5 or a 6 - the third answer. Using Microsoft Excel (show all formulas). What is the probability they will get:

a) Exactly 3 correct answers

b) No correct answers

c) At least 2 correct answers

Answer 1

Here' the answer to the question. please write back in case you've questions on the answer below.

The probability of choosing an answer is 1/3 , because each option is chosen among 3 options is chosen with a probability of 1/3.

Hence, correct answer is chosen with 1/3 probability, and a wrong answer is chosen with a probability of 1-1/3 = 2/3

We will use this to answer the questions, below.

We will use binomial distribution' pdf function in Excel : = BINOMDIST( x, n, p, TRUE/FALSE).

where,

n = total trials

x = number of success

p = probability of success

TRUE - cumulative, FALSE - probability value

Using the above formula to the parts:

a.

P(X=3 out of 6)

= 6C3 * ( 1/3)^3 *( 2/3)^3

= BINOMDIST(3, 6, .333, FALSE )

= .2191

b.

P(X = 0 out of 6)

= 6C0 * ( 1/3)^0 *( 2/3)^6

= BINOMDIST(0,6,.333, FALSE)

= 0.0881

c.

P(X>=2)

= 1- P(X=0,1)

= 1- P(X<=1)

= 1- BINOMDIST(1,6,.333, TRUE)

= 0.6482