Question

A student takes an exam containing 19 true or false questions. At least 13 correct answers are required to pass. If the student guesses, what is the probability that he will pass? Round your answer to four decimal places.

Answer 1

Answer:

Given,

let us consider,

Binomial distribution P(X = r) = nCr*p^r*q^(n-r)

p = 0.5

p + q = 1

q = 1 - p

= 1 - 0.5

= 0.5

sample n = 19

P(X >= 13) = P(X = 13) +  P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19)

= 19C13*0.5^13*0.5^6 + 19C14*0.5^14*0.5^5 + 19C15*0.5^15*0.5^4 + 19C16*0.5^16*0.5^3 + 19C17*0.5^17*0.5^2 + 19C18*0.5^18*0.5 + 19C19*0.5^19

= 0.0518 + 0.0222 + 0.0074 + 0.00185 + 0.0003 + 0.00004 + 0.000002

= 0.083592

= 0.0836