A student has been able to correctly answere true-false questions on quizzes 80% of the time.?

if he had a quiz with 5 true-false questions, what is the probability that he will correctly answer exactly 3 questions?A student has been able to correctly answere true-false questions on quizzes 80% of the time.?
this is a case of the binomial distribution


n = number of ';trials'; = 5


p = probability of ';success'; in a single trial = 0.8


q = 1 - p = probability of ';failure'; in a single trial = 0.2





the formula for k successes in n trials is


P[k] = nCk * p^k * q^(n-k)





so P[3] = 5C3 * 0.8^3 * 0.2^2





= 0.2048 or 20.48%


---------------------------A student has been able to correctly answere true-false questions on quizzes 80% of the time.?
There are ten ways he can get exactly three right:


FFTTT


FTFTT


FTTFT


FTTTF


TFFTT


TFTFT


TFTTF


TTFFT


TTFTF


TTTFF





Each of these 10 ways has a probability of 0.8 脳 0.8 脳 0.8 脳 0.2 脳 0.2 = 0.02048


So, the total probability of getting exactly three correct is: 0.2048, or 20.48%, or 128/625
I have no idea what the question part asks?





But probability he gets exactly 3 questions right:





5C3*(1/32)





10/32=.3125





so 31.25%