Probability

[swerve]

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects two 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. \(1/25\)

The OA is C

GMAT Prep

[Brent@GMATPrepNow]

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects two 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. \(1/25\)

The OA is C

GMAT Prep

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)

Cheers,
Brent

[Brent@GMATPrepNow]

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects two 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. \(1/25\)

The OA is C

GMAT Prep

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

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

Cheers,
Brent

[Scott@TargetTestPrep]

Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects two 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. \(1/25\)

The OA is C

GMAT Prep

Solution:

The probability that Kim will select two shoes of the same color is:

2/10 x 1/9 x 5 = 1/45 x 5 = 1/9

Alternate solution:

Since the first shoe she picks does not matter, then the probability of picking the first shoe is 10/10 = 1. However, since only 1 shoe is left to match the color of that shoe, the probability of picking the second shoe matching the color of the first one is 1/9. Therefore, the probability that Kim will pick two shoes of the same color is 1 x 1/9 = 1/9.

Answer: C