It is currently 19 Mar 2019, 18:51

### 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

# A certain candy store sells jellybeans in the following six

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5834
Followers: 93

Kudos [?]: 1141 [0], given: 5438

A certain candy store sells jellybeans in the following six [#permalink]  01 Aug 2018, 10:30
Expert's post
00:00

Question Stats:

28% (01:08) correct 72% (01:31) wrong based on 25 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

_________________
Director
Joined: 20 Apr 2016
Posts: 824
WE: Engineering (Energy and Utilities)
Followers: 10

Kudos [?]: 601 [1] , given: 121

Re: A certain candy store sells jellybeans in the following six [#permalink]  03 Aug 2018, 21:10
1
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 https://greprepclub.com/forum/rules-for ... -1083.html

Director
Joined: 09 Nov 2018
Posts: 509
Followers: 0

Kudos [?]: 21 [0], given: 1

Re: A certain candy store sells jellybeans in the following six [#permalink]  18 Nov 2018, 18:03
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 107 [0], given: 4

Re: A certain candy store sells jellybeans in the following six [#permalink]  18 Nov 2018, 20:02
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 [?]: 41 [0], given: 22

Re: A certain candy store sells jellybeans in the following six [#permalink]  08 Jan 2019, 23:56
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!
Re: A certain candy store sells jellybeans in the following six   [#permalink] 08 Jan 2019, 23:56
Display posts from previous: Sort by