Question

A box contains 5 white tags numbered 1 to 5, 5 red tags numbered from 1 to 5, and 5 green tags numbered from 1 to 5. If two tags are selected at random and without replacement what is the probability that both are the same number?

Answer 1

`1/7`

Explanation:

The probability of an event occurring given a finite number of possible outcomes may be calculated as
`P(event) = "number of ways event could occur"/"number of possible results"`

There are `15` possible ways to pick the same number, as you can have either white and red, red and green, or white and green for any one of the `5` numbers.

The number of ways to pick two items from a set of fifteen is

`C(15, 2) = (15!)/(2!(15-2)!) = (15*14)/2 = 105`

Thus the probability of choosing the same number is

`15/105 = 1/7`