Finite math

Question

linda took a multiple choice test. Each question had five possible answers. She guessed on four of the questions. Make up a probability distribution for the number of correct guessEd. What is the probability that she got at least two of them right? What is the probability she did not get all of them right?

Answer 1

For each question she guessed on, Linda had a 1/5 chance of picking the right answer and a 4/5 chance of picking the wrong answer.

 

 

Probability Linda got none of the four questions correct:

 

(4/5)(4/5)(4/5)(4/5) = 0.4096

 

 

Probability Linda got one of the four questions correct (remember, she could have gotten any one of the four correct, so we must take that into account):

 

(four choose one)(1/5)(4/5)(4/5)(4/5) = (4)0.1024 = 0.4096

 

 

Probability Linda got two of the four questions correct:

 

(four choose two)(1/5)(1/5)(4/5)(4/5) = (6)0.0256 = 0.1536

 

 

Probability Linda got three of the four questions correct:

 

(four choose three)(1/5)(1/5)(1/5)(4/5) = (4)0.0064 = 0.0256

 

 

Probability Linda got four of the four questions correct:

 

(1/5)(1/5)(1/5)(1/5) = 0.0016

 

 

Let's add these probabilities together to make sure they equal 1. Otherwise, we've done something wrong:

 

0.4096 + 0.4096 + 0.1536 + 0.0256 + 0.0016 = 1

 

 

 

The probability Linda got at least two right is:

 

(probability she got two right) + (probability she got three right) + (probability she got four right) =

0.1536 + 0.0256 + 0.0016 =

0.1808

 

 

The probability Linda didn't get all of them right is:

 

(probability she got none right) + (probability she got one right) + (probability she got two right) + (probability she got three right) =

0.4096 + 0.4096 + 0.1536 + 0.0256 =

0.9984