A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement,

This topic has expert replies
Moderator
Posts: 6242
Joined: 07 Sep 2017
Followed by:20 members

A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement,

by BTGmoderatorDC » Thu Nov 04, 2021 10:16 pm

00:00

A

B

C

D

E

Global Stats

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

OA B

Source: Magoosh

GMAT/MBA Expert

GMAT Instructor
Posts: 15949
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

Re: A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement,

by [email protected] » Fri Nov 05, 2021 6:54 am
BTGmoderatorDC wrote:
Thu Nov 04, 2021 10:16 pm
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

OA 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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

GMAT/MBA Expert

GMAT Instructor
Posts: 6365
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:26 members

Re: A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement,

by [email protected] » Wed Nov 10, 2021 10:12 pm
BTGmoderatorDC wrote:
Thu Nov 04, 2021 10:16 pm
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

OA B

Source: Magoosh
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.