# math

posted by .

The numbers 1 to 100 are placed in a box. You randomly select 15 numbers without looking. What is the probability that two pairs out of these 15 numbers will have the same difference?

• math -

Try to select 15 numbers among the 100, such that the difference between successive numbers are distinct!

If you cannot, the probability is 1.0!

• math -

For example, take successive differences of 1,2,3,4,5....14, we get
1,2,4,7,11,16,22,29,37,46,56,67,79,92,105
(105 is the 15th number), so it is not possible to have 14 distinct difference using numbers between 1 and 100.
This is not even counting 7-2=5, 16-11=5, etc.
Since it is impossible to select 15 numbers between 1 and 100 such that the successive differences are distinct, we are always able to choose two pairs of numbers out of any 15 numbers such that the differences are equal.
The probability is therefore 1.

## Similar Questions

1. ### Int Algebra

The difference of two numbers is 7. The sum of the numbers is -1. What are the numbers?
2. ### Math

Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole …
3. ### Math

Hot numbers in a lottery are numbers that keep coming up. Cold numbers are numbers that have not "hit" in awhile.Some people select hot numbers or cold numbers when buying a ticket. Using probability,explain whether this makes sense. …
4. ### Math

List the common multiples from 1 to 100 for each pair of numbers. Then find the least common multiple for each pair. 8 and 12, 3 and 15, 7 and 11, 9 and 10, 24 and 36, 20 and 25, 42 and 14, 30 and 12 Then find pairs of numbers for …
5. ### math

A bag contains ﬁfty slips (small pieces of paper) with the numbers 1, 2, . . . , 50 written on them (One number on each slip!). Your friend writes down ten numbers from 1, 2, . . . , 50 on a sheet of paper, and then you drawâ€”without …
6. ### Statistics

We are given this table which is Benford law for these questions they are used for filling your taxes: k= p(X=k) 1 0.301 2 0.176 3 0.125 4 0.097 5 0.079 6 0.067 7 0.058 8 0.051 9 0.046 1.) If you select two numbers randomly from any …
7. ### Statistics

A box contains five numbered balls (1,2,2,3 and 4). We will randomly select two balls from the box (without replacement). (a) The outcome of interest is the number on each of the two balls we select. List the complete sample space …
8. ### math

A. Find 3 pairs of numbers for which the least common multiple equals the product of the the 2 numbers. B. Look at the pairs of numbers you found in part a. What is true about all 3 pairs of numbers?
9. ### Math

Find three pairs of numbers for which the LCM (least common multiple) is the product of the two numbers; The pairs and LCMs are: 8 and 12: 24; 3 and 15: 15; 7 and 11: 77; 9 and 10: 90; 24 and 36: 72; 20 and 25: 100; 14 and 42: 42; …
10. ### Math/Applied

There are 9 numbers (1-9) placed in a bag, if two numbers are drawn without replacement in succession, find the probability that the sum of the numbers is odd?

More Similar Questions