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Kim has 5 pairs of shoes; each pair is a different color
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20 Dec 2015, 19:40

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E

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80% (00:57) correct 20% (00:54) wrong based on 184 sessions

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Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

Re: Kim has 5 pairs of shoes; each pair is a different color
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20 Dec 2015, 19:54

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NoHalfMeasures wrote:

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

(A) 2/5 (B) 1/5 (C) 1/9 (D) 1/10 (E) 1/25

Can be tackled in this way as well: Probability of selecting any 1 out of 10 shoes = 10/10 = 1

Probability of selecting the next shoe (out of 9 available) having the same color = 1/9 (as after selecting the 1st one, there is only 1 another shoe left with the same color).

Re: Kim has 5 pairs of shoes; each pair is a different color
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07 Dec 2017, 11:17

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NoHalfMeasures wrote:

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

(A) 2/5 (B) 1/5 (C) 1/9 (D) 1/10 (E) 1/25

P(matching pair) = P(select ANY shoe for 1st selection AND select matching shoe for 2nd selection) = P(select ANY shoe for 1st selection) x P(select matching shoe for 2nd selection) = 1 x 1/9 = 1/9 = C

ASIDE: Once we have selected ANY shoe as the 1st selection, there are 9 shoes remaining. Of those 9 remaining shoes, only 1 matches the first shoe (thus the 1/9)

Re: Kim has 5 pairs of shoes; each pair is a different color
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07 Dec 2017, 11:19

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NoHalfMeasures wrote:

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?

(A) 2/5 (B) 1/5 (C) 1/9 (D) 1/10 (E) 1/25

Here's an approach that uses counting techniques

P(matching pair) = (number of ways to get a matching pair)/(TOTAL number of ways to select 2 shoes)

number of ways to get a matching pair There are 5 different colors. So, there are 5 different ways to get a matching pair

TOTAL number of ways to select 2 shoes There are 10 shoes altogether. Since the order in which we select the 2 shoes does not matter, we can use combinations. We can select 2 shoes from 10 shoes in 10C2 ways 10C2 = 45

Aside: If anyone is interested, we have a video on calculating combinations (like 10C2) in your head. (see below)

So, P(matching pair) = 5/45 = 1/9 = C

RELATED VIDEO

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Re: Kim has 5 pairs of shoes; each pair is a different color &nbs
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07 Dec 2017, 11:19