Question

Pick a number 1 through 20. Now do it again.Now do it a third time. I am going to writedown my prediction of what numbers youpicked. Assuming no magic was used, what isthe probability I guessed right? Put youranswer in fraction form. (Note: Numbers CANbe used more than once.)

Answer 1

There are 20 numbers to choose from. Thus, the total sample space is 20.

If you choose one number, the probability of choosing that number is:

`(1)/(20)`

Now, if after choosing one number in the first round, you proceed to choose another number in the second round.

The probability of choosing a number for this second round will be:

`(1)/(20)`

Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.

For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:

`(1)/(20)`

The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.

Thus the final answer:

`(1)/(20)*(1)/(20)*(1)/(20)=(1)/(8000)`

Therefore, the final answer is:

`(1)/(8000)`