 It is currently 28 Sep 2020, 04:12 ### 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

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. # A certain candy store sells jellybeans in the following six  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 13382
Followers: 292

Kudos [?]: 3402 , given: 12228

A certain candy store sells jellybeans in the following six [#permalink]
Expert's post 00:00

Question Stats: 31% (01:35) correct 68% (01:39) wrong based on 48 sessions
A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?

A. $$\frac{1}{6}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{5}$$

D. $$\frac{1}{2}$$

E. $$\frac{3}{4}$$
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. VP Joined: 20 Apr 2016
Posts: 1302
WE: Engineering (Energy and Utilities)
Followers: 22

Kudos [?]: 1312  , given: 251

Re: A certain candy store sells jellybeans in the following six [#permalink]
2
KUDOS
Carcass wrote:
A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?

A. $$\frac{1}{6}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{5}$$

D. $$\frac{1}{2}$$

E. $$\frac{3}{4}$$

Here,

In this type we find the probability of no grape then 1 - probability of no grape will give the answer

To start with let us take the first option of the box containing 2 flavors:

Therefore the probability of box containing 2 flavors = $$\frac{1}{3}$$(Since there are 3 box containing 2 flavors, 3 flavors or 4 flavors)

Now probability of no grape in that box = $$\frac{5}{6} * \frac{4}{5} = \frac{2}{3}$$.

Therefore the probability of having 2 flavors and no grape = $$\frac{1}{3} * \frac{2}{3}= \frac{2}{9}$$.

the probability of box containing 3 flavors = $$\frac{1}{3}$$(Since there are 3 box containing 2 flavors, 3 flavors or 4 flavors)

Probability of no grape in the 3 flavor box = $$\frac{5}{6} * \frac{4}{5} * \frac{3}{4} = \frac{1}{2}$$.

Therefore the probability of having 2 flavors and no grape = $$\frac{1}{3} * \frac{1}{2}= \frac{1}{6}$$.

the probability of box containing 4 flavors = $$\frac{1}{3}$$(Since there are 3 box containing 2 flavors, 3 flavors or 4 flavors)

Probability of no grape in the 4 flavor box = $$\frac{5}{6} * \frac{4}{5} * \frac{3}{4} * \frac{2}{3} =\frac{1}{3}$$.

Therefore the probability of having 4 flavors and no grape = $$\frac{1}{3} * \frac{1}{3} = \frac{1}{9}$$.

Therefore probability of no grape in 2, 3 or 4 flavor box = $$\frac{2}{9} + \frac{1}{6} + \frac{1}{9} = \frac{1}{2}$$.

Therefore the probability of having grape in any given box = $$1 - \frac{1}{2} = \frac{1}{2}$$.
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Director Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 56 , given: 1

Re: A certain candy store sells jellybeans in the following six [#permalink]
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 176 , given: 4

Re: A certain candy store sells jellybeans in the following six [#permalink]
Expert's post
AE wrote:

Carcass wrote:
A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?

A. $$\frac{1}{6}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{5}$$

D. $$\frac{1}{2}$$

E. $$\frac{3}{4}$$

Let us choose that none are grape jellybeans..
1) when the box contains 2 flavours -
total ways - $$T_1=6C2=15$$ and without jelly beans - $$W_1=5C2=10$$
2) when the box contains 3 flavours -
total ways - $$T_2=6C3=20$$ and without jelly beans - $$W_2=5C3=10$$
3) when the box contains 4 flavours -
total ways - $$T_2=6C4=15$$ and without jelly beans - $$W_2=5C4=5$$

Probability that jelly is not there = $$\frac{W_1+W_2+W_3}{T_1+T_2+T_3}=\frac{10+10+5}{15+20+15}=\frac{25}{50}=\frac{1}{2}$$
so Probability that jelly is there = $$1-\frac{1}{2}=\frac{1}{2}$$

D
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Manager  Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 67  , given: 22

Re: A certain candy store sells jellybeans in the following six [#permalink]
1
KUDOS
Expert's post
chetan2u wrote:
AE wrote:

Carcass wrote:
A certain candy store sells jellybeans in the following six flavors only: banana, chocolate, grape, lemon, peach and strawberry. The jellybeans are sorted into boxes containing exactly 2, 3 or 4 different flavors, with each possible assortment of flavors appearing in exactly one box. What is the probability that any given box contains grape jellybeans?

A. $$\frac{1}{6}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{5}$$

D. $$\frac{1}{2}$$

E. $$\frac{3}{4}$$

Let us choose that none are grape jellybeans..
1) when the box contains 2 flavours -
total ways - $$T_1=6C2=15$$ and without jelly beans - $$W_1=5C2=10$$
2) when the box contains 3 flavours -
total ways - $$T_2=6C3=20$$ and without jelly beans - $$W_2=5C3=10$$
3) when the box contains 4 flavours -
total ways - $$T_2=6C4=15$$ and without jelly beans - $$W_2=5C4=5$$

Probability that jelly is not there = $$\frac{W_1+W_2+W_3}{T_1+T_2+T_3}=\frac{10+10+5}{15+20+15}=\frac{25}{50}=\frac{1}{2}$$
so Probability that jelly is there = $$1-\frac{1}{2}=\frac{1}{2}$$

D

This explanation was amazing! A real Eye opener!
Intern Joined: 11 Jan 2020
Posts: 5
Followers: 0

Kudos [?]: 0 , given: 3

Re: A certain candy store sells jellybeans in the following six [#permalink]
Can you explain why we are solving it through 1-P (atleast scenario) method? GRE Instructor Joined: 10 Apr 2015
Posts: 3838
Followers: 149

Kudos [?]: 4499  , given: 69

Re: A certain candy store sells jellybeans in the following six [#permalink]
1
KUDOS
Expert's post
kanny wrote:
Can you explain why we are solving it through 1-P (atleast scenario) method?

The solution by @pranab223 uses the complement (i.e, the probability of selecting a box with grape flavor = 1 - the probability of NOT selecting a box with grape flavor)

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Intern Joined: 07 Jun 2020
Posts: 2
Followers: 0

Kudos [?]: 1  , given: 0

Re: A certain candy store sells jellybeans in the following six [#permalink]
1
KUDOS
There is ambiguity in this question, it is said that each of the flavor appears in exactly one box. So it can be understood as 3 boxes with 2 flavors each or 2 boxes with three flavors each or 2 boxes with 4 flavors in one and 2 flavors in another. Re: A certain candy store sells jellybeans in the following six   [#permalink] 07 Jun 2020, 06:10
Display posts from previous: Sort by

# A certain candy store sells jellybeans in the following six  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.