Question

A multiple-choice quiz has 15 questions, each with 4 possible answers of which only 1 is the correct answer. What is the probability that a student gets
a. exactly 10 correct answers
b. at least 1 correct answer
c. 8 to 12 correct answer

Answer 1

binomial distribution for each of these

Answer 2

\[p=\frac{1}{4},1-p=\frac{3}{4}\]
\[P(x=10)=\binom{15}{10}\left (\frac{1}{4}\right)^{10}\left(\frac{3}{4}\right)^5\]

Answer 3

b) at least one means not none
\[1-\left(\frac{3}{4}\right)^{15}\]

Answer 4

8 to twelve has no shortcut, gotta add them all up

Answer 5

add?

Answer 6

c