A box contains 75 balls numbered from 1 to 75 If 7 balls are drawn with replacement what is the probability that at least two of them have the same number?

Answer 1

25.1%

The probability of having at least two same number balls when 7 balls are drawn with

replacement from a box containing 75 numbered balls from 1 to 75 is calculated as

follows:

We calculate the probability of drawing 7 times a ball (with replacement) and having

all different numbers. Then we subtract this value from 1. This will be the probability

of all the possibilities of combinations of 7 numbers where at least two are repeated.

1.- For the 1st ball the options are 75/75.

2.- For the 2nd ball the options for not repeating the 1st number are 74/75.

3.- For the 3rd ball the options for not repeating the previous two numbers are 73/75.

4.- For the 4th ball the options for not repeating the previous three numbers 72/75.

5.- For the 5th ball ........................................................................... 71/75.

6.- For the 6th ball ........................................................................... 70/75.

7.- For the 7th ball ........................................................................... 69/75.

The probability of drawing seven balls (with replacement) having all different numbers

is: 75/75(74/75)(73/75)(72/75)(71/75)(70/75)(69/75) = 0.749419476...

The probability of having at least two same number balls when 7 balls are drawn with replacement from the given box is:

P = 1 - 0.749419476... = 0.250580524...≈ 25.1%