tricky probability

[mariah]

There are five pairs of shoes with different colors in a box. If two shoes are to be selected from the box without replacement, what is the probability that they have the same color?

1/9
2/9
1/3
3/8
2/3

please come with explanations

[RickH]

What's the correct answer?

[Maciek]

Hi Mariah!

it is great question. Thank you for posting it.

IMO A

The formula for finding the probability of an event A:
P(A) = the number of ways event A can occur / the total number of possible outcomes

A - two shoes, that were selected from the box without replacement, have the same color

There are five pairs of shoes with different colors in a box

so 5 is the number of ways event A can occur

We find the the total number of possible outcomes with combination formula

combination formula
A formula for the number of possible combinations of r objects from a set of n objects.


Please read the lesson:
https://www.beatthegmat.com/mba/2010/08/ ... -your-head

10C2 = 10*9/2 = 45

Let us plug in the numbers

P(A) = 5/45 = 1/9

I choose answer A.

hope it helps!

[Ian Stewart]

Or you can look at it this way: no matter what shoe you pick first, there are 9 shoes left, exactly 1 of which matches your first selection. So the probability of getting two matching shoes must be 1/9.