NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 13:25 It is currently 26 Apr 2024, 13:25
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

There are two bags with red and green balls only, the first bag contai

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
B
JourneyToTheTop
Intern
Intern
Joined: 23 Sep 2016
Posts: 46
Own Kudos [?]: 9 [4]
Given Kudos: 23
Location: Canada
Concentration: Strategy, Technology
Schools: Ivey '21 (A$)
GMAT 1: 640 Q42 V37
GPA: 2.7
Send PM
There are two bags with red and green balls only, the first bag contai [#permalink] New post   24 Sep 2018, 11:53
4
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

69% (02:24) correct 31% (02:14) wrong based on 80 sessions
Hide Show timer Statistics
There are two bags with red and green balls only, the first bag contains 4 red and 6 green balls, second contains 3 red and 7 green balls. Andy picked 1 ball from the first bag and placed it in the second bag, then Mira picked a ball from the second bag. What is the probability that Mira picked a red ball?

A) 8/55
B) 17/55
C) 9/55
D) 1/3
E) 23/110

Show SpoilerWorking below
This was my work:

First bag P(Red) * second bag P(Red) = 4/10*4/11 = 16/110 = 8/55
First bag P(Green) * second bag P(Red) = 6/10*3/11 = 18/110 = 9/55

Answer = 8/55 + 9/55 = 17/55
ShowHide Answer
Official Answer
B
User avatar
B
alldaytestprep
Tutor
Joined: 08 May 2018
Affiliations: All Day Test Prep
Posts: 98
Own Kudos [?]: 88 [1]
Given Kudos: 1
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49
GRE 1: Q167 V167
GPA: 3.58
Send PM
Re: There are two bags with red and green balls only, the first bag contai [#permalink] New post   24 Sep 2018, 12:22
1
Kudos
Expert Reply
JourneyToTheTop wrote:
There are two bags with red and green balls only, the first bag contains 4 red and 6 green balls, second contains 3 red and 7 green balls. Andy picked 1 ball from the first bag and placed it in the second bag, then Mira picked a ball from the second bag. What is the probability that Mira picked a red ball?

A) 8/55
B) 17/55
C) 9/55
D) 1/3
E) 23/110

Show SpoilerWorking below
This was my work:

First bag P(Red) * second bag P(Red) = 4/10*4/11 = 16/110 = 8/55
First bag P(Green) * second bag P(Red) = 6/10*3/11 = 18/110 = 9/55

Answer = 8/55 + 9/55 = 17/55



The probability of picking a red from second bag depends on whether or not a red or green is moved from the first bag. There is a 4/10 chance a red is picked from first bag and a 6/10 chance a green is picked.

If a red is picked from first bag there is a 4/11 chance of picking a red from second bag.

If a green is picked from first bag there is a 3/11 chance of picking a red from second bag

Therefore there is a 40% chance of having a 4/11 chance of picking a red OR there is a 60% chance of having a 3/11 chance of picking a red

(4/10)(4/11) + (6/10)(3/11) = (16/110) + (18/110) = 34/110 = 17/55

Answer: B
User avatar
G
pandeyashwin
Manager
Manager
Joined: 14 Jun 2018
Posts: 171
Own Kudos [?]: 257 [0]
Given Kudos: 176
Send PM
Re: There are two bags with red and green balls only, the first bag contai [#permalink] New post   25 Sep 2018, 02:28
There are two possbilities :
1. Andy picks up a red ball and transfers it to the second bag.
2. Andy picks up a green ball and transfers it to the second bag.

Probability of Andy picking up a red ball and then Mira picking up a red ball = 4/10 * 4/11 (4/11 because Andy transfers the red ball to the second bag)

Probability of Andy picking up a green ball and then Mira picking up a red ball = 6/10 * 3/11 (Total ball increases but not the red ball because Andy transferred a green ball)

Probability = 4/10*4/11 + 6/10*3/11 = 34/110 = 17/55
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14831
Own Kudos [?]: 64940 [1]
Given Kudos: 427
Location: Pune, India
Send PM
Re: There are two bags with red and green balls only, the first bag contai [#permalink] New post   25 Sep 2018, 04:27
1
Kudos
Expert Reply
JourneyToTheTop wrote:
There are two bags with red and green balls only, the first bag contains 4 red and 6 green balls, second contains 3 red and 7 green balls. Andy picked 1 ball from the first bag and placed it in the second bag, then Mira picked a ball from the second bag. What is the probability that Mira picked a red ball?

A) 8/55
B) 17/55
C) 9/55
D) 1/3
E) 23/110

Show SpoilerWorking below
This was my work:

First bag P(Red) * second bag P(Red) = 4/10*4/11 = 16/110 = 8/55
First bag P(Green) * second bag P(Red) = 6/10*3/11 = 18/110 = 9/55

Answer = 8/55 + 9/55 = 17/55


The question may look complicated but it is not.
There are two events that take place in sequence. The probability of the second event depends on the result of the first event.

We just need to consider the two results of the first event separately. It is like a partial binomial tree.

Attachment:
BT.jpeg
BT.jpeg [ 37.93 KiB | Viewed 3425 times ]


Probability of picking a Red from second bag = (4/10)*(4/11) + (6/10)*(3/11) = 17/55
GMAT Club Bot
gmatclubot
Re: There are two bags with red and green balls only, the first bag contai [#permalink]
25 Sep 2018, 04:27
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions