Probability

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Probability

by swerve » Tue Mar 17, 2020 7:48 am

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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

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Source: Beat The GMAT — Problem Solving | Tue Mar 17, 2020 7:48 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: Probability

by Brent@GMATPrepNow » Wed Mar 18, 2020 5:47 am

swerve wrote: ↑
Tue Mar 17, 2020 7:48 am
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 Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: Probability

by Brent@GMATPrepNow » Wed Mar 18, 2020 5:47 am

swerve wrote: ↑
Tue Mar 17, 2020 7:48 am
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

Brent Hanneson - Creator of GMATPrepNow.com

Quote

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Probability

by Scott@TargetTestPrep » Wed Mar 18, 2020 3:46 pm

swerve wrote: ↑
Tue Mar 17, 2020 7:48 am
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

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