Question

A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question what is the probability that the student will pass the test

Answer 1

Solution:

Each question has two options. TRUE and FALSE

So , probability of answer is correct = 1/2 = 0.5

p = 0.5

Test consists of 10 questions.

n = 10

Let X be the number of correct answered questions.

X follows Binomial(10 , 0.5)

PMF of binomial is

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}  

To pass the test a student must answer at least eight questions correctly.

$\therefore$ P(the student will pass the test)

= P(X $\geq$ 8)

= P(X = 8) + P(X = 9) + P(X = 10)

=  (₁₀ C ₈) * 0.5⁸ * (0.5)^10-8 + (₁₀ C ₉) * 0.5⁹ * (0.5)^10-9 +  (₁₀ C ₁₀) * 0.5¹⁰ * (0.5)^10-10

=  0.0439453125 + 0.009765625 + 0.0009765625

= 0.0546875