Jeanine's Shoes
Jeanine has two pairs of red shoes, two pairs of green shoes, and two pairs of blue shoes. If Jeanine goes to her closet and randomly selects two shoes, what is the probability that Jeanine will have a pair of shoes that are of the same color and that are wearable?
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1 solution
I am getting 1 1 1 .
Their are total 6 pair of shoes, i.e. { R 1 , R 1 } , { R 2 , R 2 } , { B 1 , B 1 } , { B 2 , B 2 } , { G 1 , G 1 } , { G 2 , G 2 } .
Probability of getting correct pair = ( 2 1 2 ) ( 1 6 ) = 1 1 1
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I should clarify that the either of the two left-footed red shoes can pair with a red right-footed red shoe.
You have to multiply by 2 bc each right foot has two left foot options
The trick to this question is remembering that there are left and right shoes!
For the purposes of "selecting two shoes", we can think of Jeanine as having picking one shoe, then another shoe after the first. In this case, it doesn't matter which shoe Jeanine selects first. However, for any given shoe she chooses, there will only be two shoes of the same color and that will fit on the other foot (the third shoe of that color will give her either two left or two right shoes).
With only 2 shoes that work out of the remaining 11, the probability is 1 1 2 .