Question

in a final exam you have four multliple choice questions left to do. each questions has five suggested answers and only one of the answers in correct. assuming that your answers are randomly selected what is the probability that you get zero, one, or three questions correct?

Answer 1

The probability that you get zero questions correct is 0.4096

The probability that you get one questions correct is 0.4096

The probability that you get three questions correct is 0.0256

Explanation:

These probability can be describe with a Binomial Distribution. These distribution can be used when we have n identical and independent situations in which there is a probability p or probability of success and a probability q or probability of fail. Additionally q is equal to 1 - p. The probability of x for a situation in which we can apply binomial distribution is:

`P( x,n,p) = n Cx * p^(x ) * q^ {n-x}`

Where x is the variable that says the number of success in the n situations

And nCx is calculate as:

`nC x = ( n!)/( x! (n-x)! )`

From the question we can identify that:

• n is equal to 4 multiple choice question
• p is 1/5 or 0.2, the probability of get one question correct
• q is 4/5 or 0.8, the probability of get one question incorrect

Then the probability of get zero questions correct of 4 questions is:

`P( 0, 4, 0.2) = 4 C0 * p^(0 ) * q^ {4-0}= 0.4096`

The probability of get one question correct of 4 questions is:

`P( 1, 4, 0.2) = 4 C1 * p^(1 ) * q^ {4-1}= 0.4096`

The probability of get three questions correct of 4 questions is:

`P( 3, 4, 0.2) = 4 C3 * p^(3 ) * q^ {4-3}= 0.0256`