Question

On a true-false test with three questions, what is the probability of guessing the answers to exactly two questions correctly?

a) 2/3
b) 3/8
c) 1/2
d) 5/8
e) 3/4

Can you clearly expain to me? Thanks.

Answer 1

each question has a probability of \(\frac{1}{2}\) to answer correctly, since there are only two choices and apparently you can only guess.
since there are three questions, each with two possible answers, there are a total of \(2^3=8\) different ways to answer and each outcome therefore has probability of \((\frac{1}{2})^3=\frac{1}{8}\)
you want to know what the probability you get exactly two right
there are 3 ways to do this, and we can count them
right, right, wrong
right, wrong, right,
wrong, right, right.

so of the total you have 3 possible ways to answer two correctly, and your probability of getting exactly 2 right is \(\frac{3}{8}\)

Answer 2

The probability of guessing a question correctly in 1 question is 1 in 2. This is combinatorics. The total possibilities are 2 * 2 * 2 = 8
Now we must have 2 questions correctly done, and we can do this by filling the slots. Let's say that we have C1 and C2, and we have them in different slots of 3.
No need to type more as satellite has answered lol