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 color?

Answer 1

Let's begin by saying that the numbers on the tags are not important.

Explanation:

For the first draw even the colour is not important.
For the second draw we want the same colour as in the first draw. There are four tags left with that colour, so the probability of drawing one is 4 on a total of 14.
`P=4/14=2/7~~28.6%`

Answer 2

`P(2 same) = 2/7`

Explanation:

There are 3 ways in which 2 tags can be the same colour:

Both white, both red or both green.

`P(same) = P(WW) + P("RR") + P(GG)`

=`5/15xx4/14 + 5/15xx4/14 + 5/15xx4/1`

= `3 xx 2/21`

=`2/7`