Statistics. Introduction. The study of probability is often deceptive: on the surface, it seems close to everyday experience and intuition seems enough to find answers to problems.
The confusion results from two sources
1) There are percentage signs in the answers
2) The fact that 50% of the answers are “25%” and 25% of the answers are “50%”
The question does not say that the answer must among the listed options. It only asks what is the probability that you will be correct if you answer at random.
The question instructs to only choose one single answer out of four. And assume a uniform distribution, since that is most likely intended, then each answer has a chance of 25% to become chosen.
So the correct answer should be: 25%.
This computes to answer A being correct, as well as answer D. Could that be?
Yes, it can. The question does not reveal how many of the four given answers are correct, but since there is one to be picked, assume that at least one of the four answers is correct.
Let's call answer A + answer D the correct answer pair.
Now, there are two possible choices (A or D) that result in 50% of the correct answer (A and D). Secondly, there is 50% chance of picking one (A or D) of two (A and D) out of four (A to D).
So whether answer A or answer D is chosen, in either case the probability of being correct (50% × 50%) is 25%, which evaluates true.
Thus, yes, the question has 2 correct answers.
Do you agree with this logic?
The question starts:
"If you choose an answer to this question at random,
However it does not then continue:
"what is the probability that the answer chosen will be the probability of choosing that answer?”
It instead says:
"what is the probability that you will be correct?"
And then doesn't define correct.
However, lets presume that one of the following answers can be chosen:
a, b, c or d
The probability of choosing each answer:
a - 25%
b - 25%
c - 25%
d - 25%
25% - 50%
50% - 25%
60% - 25%
Being correct for "what is the probability that you will be correct?" if there is one correct answer (although as covered above the question doesn't define correct or specify how many answers are correct). This produces the same answer as the question "is the answer you choose the probability of choosing that answer?”
a – yes
b - no
c - no
d - yes
25% - yes
50% - no
60% - no
Could this be the real question in the question. "what is the probability that the answer chosen will be the probability of choosing that answer?":
In which case, ‘b’ is correct!
Provided that one of the four option is correct (assumption), the probability will be 25% that you are correct.
Since you are picking up a random answer (don't bother about logic at all), the correct answer to the question "what is the probability that you will be correct" is 25%. Do not bother about the options, which is misleading.
But if there are two choices of 25% which is technically wrong because every choice must be different from the another.
Chances of each selection at random are 1/4 or 25%. That means 25% would select choice A at random, 25% choice B at random and so on. Since we know choice A and D are the correct answer (they are repeated which is wrong), that leads us to 50% correct answer if people make random choices.
So what is the probability that you will be correct is 50%
What were your assumptions?
What were your assumptions?
Did you make more than one assumption?