   SEARCH HOME Math Central Quandaries & Queries  Question from sarahbear, a student: Suppose four digits are to be randomly selected (repetitions allowed) Find the probability that A. 5562 is selected B. 0000 is selected C. All four digits are the same D. 2 is the first digit selected Hi,

I can help get you started.

There are 10 choices for the first digit selected, 10 for the second digit and so on. Thus there are $10 \times 10 \times 10 \times 10 = 10^4$ possible outcomes. Another way to see this is to think about listing the possible outcomes in a logical order. I would list them as

0000
0001
0002
.
.
0009
0010
0011
0012
.
.
9999

There are 10,000 items in the list.

For part A. Look at the list. How many times does 5562 appear in the list. Once! Thus the probability that you chose 5562 is 1 in 10,000 or $\large \frac{1}{10,000}.$

For part C. Again look at the list. How many items in the list have all four digits the same?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.