Write all possible outcomes of guessing the answers of two true-false questions. Then compare with the given solution.
See solution.
Practice makes perfect
We are told that a student randomly guesses the answers to two true-false questions. Besides that, we are given an statement about finding the probability of the student guessing both answers correctly.
We will describe and correct the error in the given answer. We will first find the total outcomes of the given event. Let T represent guessing the answer correctly and F represent guessing the answer incorrectly.
Guessing the First Answer
Guessing the Second Answer
Outcome
T
T
TT
T
F
TF
F
T
FT
F
F
FF
Since guessing the first answer correctly and the second answer incorrectly is different from guessing the first answer incorrectly and the second one correctly, we will count these outcomes separately. Therefore, the total number of the outcomes is 4. Also, the number of favorable outcomes is 1, that is guessing both answers correctly. Now we will write the probability.
P(Guessing the both answers correctly)=1/4
The given answer is wrong because they thought that guessing the first answer correctly and the second one incorrectly is the same as guessing the first answer incorrectly and the second one correctly. From here we can correct the error.
