Question

A calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. find the probability of getting at least 70% of the questions correct?

Answer 1

The probability would be 0.000017.

70% of the 20 questions is 14 questions correct. Using a binomial distribution for this, we have:


`_(20)C_(14)(0.2)^(14)* (1-0.2)^(20-14) \\ \\ (20!)/(14!6!)* (0.2)^(14) * (0.8)^6 \\ \\ \approx 0.000017`

Answer 2

1.66479*10^(-6)

Explanation:

to get 70% correct question out of 20 the student have correct 14 questions correct.

probability of getting answer correct p= 1/5=0.2

probability of getting answer wrong q= 4/5=0.8

its case of binomial distribution where

n= 20, r= 14 , p= 0.2 and q= 0.8

therefore

[tex]_{20}^{14}\textrm{C}\times 0.2^{14}\times0.8^{6}[\tex]

solving we get

1.66479*10^(-6)