A box contains 4 red chips and 2 blue chips. If two chips are

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri May 29, 2020 6:40 am

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A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10

Answer: B
Source: Magoosh

Source: Beat The GMAT — Problem Solving | Fri May 29, 2020 6:40 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: A box contains 4 red chips and 2 blue chips. If two chips are

by Brent@GMATPrepNow » Tue Jun 02, 2020 5:43 am

BTGModeratorVI wrote: ↑
Fri May 29, 2020 6:40 am
A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10

Answer: B
Source: Magoosh

P(different colors) = P(1st chip is red and 2nd chip is blue OR 1st chip is blue and 2nd chip is red)
= P(1st chip is red and 2nd chip is blue) + P(1st chip is blue and 2nd chip is red)
= P(1st chip is red) x P(2nd chip is blue) + P(1st chip is blue) x P(2nd chip is red)
= 4/6 x 2/5 + 2/6 x 4/5
= 8/30 + 8/30
= 16/30
= 8/15

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

quichopipe: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 08, 2020 12:42 pm

Re: A box contains 4 red chips and 2 blue chips. If two chips are

by quichopipe » Wed Jun 03, 2020 1:19 pm

Probability is (total of favorable outcomes)/(total number of possible outcomes).

Let's let R = a red chip and B = a blue chip. Since we need one chip from each color, we can either pick a red then a blue, or a blue then a red.
RB or BR

There are 4 possible Rs and 2 possible Bs
Case 1: (4C1)*(2C1)
Case 2: (2C1)*(4C1)

This is really just saying (4C1)*(2C1) * 2 which is 16

Now let's look at our denominator
There are 6 chips total (4+2 = 6)
We first want one chip from 6 and then one chip from 5 (no replacement)
(6C1)*(5C1) = 30

So 16/30 = 8/15

Answer choice B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A box contains 4 red chips and 2 blue chips. If two chips are

by Scott@TargetTestPrep » Sat Apr 03, 2021 10:23 am

BTGModeratorVI wrote: ↑
Fri May 29, 2020 6:40 am
A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

A. 1/2
B. 8/15
C. 7/12
D. 2/3
E. 7/10

Answer: B

Solution:

To satisfy the requirement, we must obtain either R-B or B-R. Thus, we need to determine:

P(red) x P(blue) + P(blue) x R(red)

4/6 x 2/5 + 2/6 x 4/5 = 2/3 x 2/5 + 1/3 x 4/5 = 4/15 + 4/15 = 8/15.

Answer: B

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