Question

suppose an economic examination has 3 true or false questions and a passing grade is obtained with 2 or more correct answers. a student answered all the 3 questions by flipping a fair coin and answering true if the coin shows a head and false if it shows a tail. a) write down the sample space. using the classical interpretation of probability, what is the chance the student will pass the exam?

Answer 1

Sample space (in terms of answer choices, not coin outcome with F = false, T = True)
{ FFF, FFT, FTF, FTT, TFF, TFT, TTF, TTT}

P(passing exam) = P(2 or more True answers) = 4/8 = 1/2 = 50%

Explanation:

Sample space (in terms of answer choices, not coin outcome with F = false, T = True)
{ FFF, FFT, FTF, FTT, TFF, TFT, TTF, TTT}
There are 2³ = 8 elements in the sample space

These correspond to the sample space for coin toss (H = heads, T = tails)
{ TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}

There are 4 outcomes where 2 or more questions are marked True

{ FTT , TFT , TTF, TTT}
Total of 4 elements

This corresponds to 2 or more heads:
{THH, HTH. HHT, HHH}

P(passing exam) = P(2 or more True answers) = 4/8 = 1/2 = 50%