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)

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