# What is probability?

Yh Hoo
What is probability??

If i have 1 objective question with four multiple choices. The probability of getting 1 question correct is 1/4. But how if i did 4 question, the probability of getting 1 question correct = 1.
What is meant by that?? That means i definitely will have one question done correctly amongst 4 questions ?

Studiot

the probability of getting 1 question correct = 1.

No the probability is still 1 in 4.

There are now 16 total possible answers (4 for each of 4 questions) and only 4 correct ones.

So the probability of a correct answer is 4 in 16 or 1 in 4.

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Your question isn't clear. You say you have "1 objective question" and then you ask about 4 questions.

Let's suppose you have 4 questions and that each question has 4 choices. We will assume each question has only one correct choice and that you pick a choice at random.

The probability of getting a given question correct is 1/4.

The probability of getting at least one correction correct out of 4 questions can be calculated by computing 1.0 minus the probability of missing all 4 questions.

You can also compute the probability of getting at least one question correct by using the formula for the probability of a union of events. But this formula does not say to compute (1/4 + 1/4 + 1/4 + 1/4).

Look up the formula in your course materials. They should explain formulas such as

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$
etc.

As I interpret you, you are asking that since the probability of getting a question right is 1/4, mustn't the probability of getting a question right out of 4 question be 4*1/4? The answer is no, you can't add up those probabilities like that.

This is how you do it: what is the probability for getting no answers correctly? The complement of this is to get at least one answer correctly. So if we call the probability for getting no answer correct p, then the probability you are looking for is 1-p.

Gold Member
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To be more specific, just using exactly what has already been stated, the chance of getting one question wrong is .75 so the chance of getting all 4 questions wrong is .75^4 which is about 32%. Conversely, that means that the chance of NOT getting all 4 wrong is about 68% and that is the same as saying the odds of your get AT LEAST one right is 68%. If you want the odds of getting EXACTLY one right, it's different and I'll leave that one up to you.

Homework Helper

If i have 1 objective question with four multiple choices. The probability of getting 1 question correct is 1/4. But how if i did 4 question, the probability of getting 1 question correct = 1.
Where did you get that? As others have said "1 question correct" can have many interpretations but for NONE of them is the probability 1. If you mean "exactly one question correct, the probability is $4(1/4)(3/4)^3= 27/64$ which is 0.421875. If you mean "at least one question correct", the probability is $1- (3/4)^4= 1- 81/256= 0.68359375$.

What is meant by that?? That means i definitely will have one question done correctly amongst 4 questions ?
Well, you know that isn't going to happen don't you! (If I had 4 questions and picked each of four possible responses for each, at random, I would probably get all four wrong!)

Studiot

Thanks, guys, for showing me something.

Mensanator

If i have 1 objective question with four multiple choices. The probability of getting 1 question correct is 1/4. But how if i did 4 question, the probability of getting 1 question correct = 1.
What is meant by that?? That means i definitely will have one question done correctly amongst 4 questions ?

No, there is still the possibility of getting 0 correct.

Yh Hoo

Sorry everyone! I think i am supposed to ask in this way. A objective question has 4 multiple choices. If a student do 4 objective questions by picking 1 of the 4 choices randomly, what is the number of correctly-done question expected for him ??

Gold Member
2022 Award

Sorry everyone! I think i am supposed to ask in this way. A objective question has 4 multiple choices. If a student do 4 objective questions by picking 1 of the 4 choices randomly, what is the number of correctly-done question expected for him ??

The answer to THAT question is not a number, it a probability distribution chart showing values for 0, 1, 2, 3, 4

daveb

The answer to THAT question is not a number, it a probability distribution chart showing values for 0, 1, 2, 3, 4

From what is asked (my bold) it looks like he is asking for the expectation value, which is a number.

Sorry everyone! I think i am supposed to ask in this way. A objective question has 4 multiple choices. If a student do 4 objective questions by picking 1 of the 4 choices randomly, what is the number of correctly-done question expected for him ??

Do you know how to calculate an expectation value for a probability distribution?