Probability question - can you make this easier to understand?

Question

Here's the question:

The probability of randomly guessing at the fist three multiple choice questions on an exam, each of which has four possible answers, is 0.015625. True or false?

I understand basic probability but the wording of this question really throws me off. The probability of randomly guessing? Does my prof mean randomly guessing correctly? I don't understand. Could you reword this or set it up in a way I can understand?

Answer 1

'Random' means that every possibility has an equal chance.  So suppose there were two answers to a question.  If you answered by flipping a coin, that would be random because you would be just as likely to choose either one.  With six answers you might roll a dice, just one dice (a die, actually).  With four, you are just guessing, it could be any of the four.

Well if you had one question with four answers, and only one of them was right, and you guessed randomly, you would have a 1 in 4 chance of getting the right one.  Or 25%.

If there were two such questions, your chance of getting both of them right is .25 * .25.  Or 1/16.

With three questions, it's .25 * .25 * .25, or .25 to the third power.

Answer 2

The question is worded poorly.  It should read:  When randomly guessing,  is the probability of getting the first three multiple choice questions correct on an exam (each of which has four possible answers) 0.015625?

DON'T READ FURTHER IF YOU DON'T WANT TO SEE THE ANSWER!

The probability of getting all three correct is the probability of getting the first right times the probability of getting the 2nd right times the probability of getting the 3rd right.

So, the answer is: 1/4 * 1/4 * 1/4 = 1/64 (which is, indeed, .015625)

Answer 3

How about this:

What is the probability of being correct on the

first three questions of your exam if you

randomly choose one of the four choices

given for each question ?

The way it is phrased, you might answer:

The probability of randomly guessing (or not) is a function

of how much the student studied, and we have no

information about that, so we cannot calculate the

probability.

But very few professors appreciate smarty-pants answers like that.

.