Question

A student takes a true-false test that has 12 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(10 or more)

Answer 1

Step-by-step answer:

assuming the true-false test have equal probabilities (each 0.5), we can use the binomial probability to calculate the sum of probabilities of getting 10, 11 or 12 questions correctly out of 12.

p=probability of success = 0.5

N=number of questions

x = number of correct answers

then

P(x) = C(N,x)(p^x)((1-p)^(N-x))

where C(N,x) = N!/(x!(N-x)!) = number of combinations of taking x objects out of N.

P(10) = C(12,10)(0.5^10)((1-0.5)^2) = 33/2048 = 0.01611

P(11) = C(12,11)(0.5^11)((1-0.5)^1)     =  3/1024 = 0.00293

P(12) = C(12,12)(0.5^12)((1-0.5)^0) =  1/4096 = 0.00024

for a total probability of 79/4096 = 0.01929