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There is a macaron vending machine which sells macarons of the following varieties of combinations. There are 3 different flavours of macaron shells which are green-tea, vanilla, and strawberry. There are 4 different flavours of creams which are chestnut, chocolate fudge, buttercream, and mixed berries.


 

This macaron vending machine does not let you choose which combination you want to get. The following graph shows the outcomes of different combinations of macarons the machine has every 251 macarons.


no description

 

Jared came to the vending machine to buy himself a macaron. Answer in 2 decimal places and find the possibilities of Jared getting a macaron he wants if:

 

a) Jared wants the macaron to have some sort of berries flavour in it (either with the strawberry flavoured shells or mixed berries cream or both).

 

b) Jared is happy with anything as long as the macaron does not have buttercream.

 

c) Jared is fine with anything other than the combinations of green-tea flavoured shells with any cream except chestnut cream.

 

d) Jared is fussy and only wants vanilla flavoured shells with chocolate fudge.

 

Note:

All 4 cases are separate and independent; one does not affect another.

Alternatives

The contributor suggests A is the correct option
Option Alternative First
answers
Confirmed
answers
A

a) 0.51

b) 0.71

c) 0.88

d) 0.12

8 (36.36%)

13 (100.00%)

B

a) 0.66

b) 0.71

c) 0.88

d) 0.12

4 (18.18%)

0 (0.00%)

C

a) 0.66

b) 0.71

c) 0.88

d) 0.61

5 (22.73%)

0 (0.00%)

D

a) 0.51

b) 0.71

c) 0.80

d) 0.12

5 (22.73%)

0 (0.00%)

E

a) 0.51

b) 0.29

c) 0.88

d) 0.61

0 (0.00%)

0 (0.00%)

Explanation

The following explanation has been provided relating to this question:

How did you go? I hope you enjoyed my question! Congratulations to those who chose the correct answer, which is Option A!! ((((=^0ω0^=)// *clap*clap

 

With questions like this, it is important to read carefully and correctly identify the requirements.

I will be going through the working out for all 4 cases.

I will be using the equation: ,

which means: the probability of an event = the number of the event in ratio to the total number in the sample space.

In the case of a macaron vending machine, the sample space is always 251.

 

 

Part A

a) Jared wants the macaron to have some sort of berries flavour in it (either with the strawberry flavoured shells or mixed berries cream or both).

 

Jared doesn't mind what the filling is as long as the shells are strawberry flavoured.

Jared doesn't mind what the shells are as long as the filling is mixed berries cream.

Either way, Jared will be happy; and of course, Jared will certainly be happy if he got strawberry macaron shells with mixed berries cream.

 

The highlighted area bellow shows macarons Jared will be happy with.

no description

There are 104 macarons with strawberry flavoured shells and 62 macarons with mixed berries cream.

There are 38 macarons with both strawberry flavoured shells and mixed berries cream (This is the overlap).

 

 

if you chose Option B or Option C, you might have forgotten about the overlap of strawberry flavoured shells and mixed berries cream.

 

 

Part B

b) Jared is happy with anything as long as the macaron does not have buttercream.

 

The only thing Jared cares is if the macaron has buttercream or not.

Jared is happy as long as the fillings are chestnut cream, chocolate fudge, or mixed berries cream.

Jared is happy with any shells for his macaron.

 

The highlighted area bellow shows macarons Jared will be happy with.

no description

There are 74 macarons with buttercream filling which Jared does not want.

 

 

if you chose Option E, you might have misread the case, and thought Jared only wanted macarons with buttercream, while in fact, Jared wanted the complimentary, macarons without buttercream.

 

 

Part C

c) Jared is fine with anything other than the combinations of green-tea flavoured shells with any cream except chestnut cream.

 

Jared is fine with any macaron as long as the shells are either vanilla flavoured or strawberry flavoured.

Jared is also fine with another type of macaron which has green-tea flavoured shells with chetnut cream, and Jared does not like any other fillings with green-tea flavoured shells.

 

The highlighted area bellow shows macarons Jared will be happy with.

no description

There are 96 macarons with vanilla flavouredshells and 104 macarons with strawberry flavoured shells.

There are 20 macarons that are green-tea flavoured shells with chestnut cream.

 

 

If you have chosen Option D, you might have missed the bit that Jared doesn't mind getting green-tea flavoured shells with chestnut cream.

 

 

Part D

d) Jared is fussy and only wants vanilla flavoured shells with chocolate fudge.

 

This is fairly straight forward. Jared only wants to have vanilla flavoured shells with chocolate fudge filling and nothing else.

 

The highlighted area bellow shows macarons Jared will be happy with.

no description

There are 31 macarons that are vanilla flavoured shells with chocolate fudge filling.

 

 

If you chose  Option C or Option E, you have misinterpreted the question and thought Jared wants any macaron as long as it has vanilla flavoured shells or chocolate fudge.

 

 

These are the 11 different macarons the vending machine offer. Which would you want?


 

I hope the explanation was clear and it helped build your confidence in this topic of probabilities. If you have any questions, objections or suggestions, please feel free to leave a comment bellow. I will be more than happy to hear from you :)

Topics

The following topics have been indicated as being relevant to this question:

Probability, Problem solving, Sample Space, Events, Tables

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Written: 7:01pm, 10 JunAuthor has: 3546 points and 24 badges

I love your question it's so cute XD

You have obviously put lots of effort into it and your explanation is so easy to follow.

(Green Tea with Chocolate Fudge all the way, it looks the cutest.)

 Written: 7:19pm, 10 JunReply written by question author
 

Thank you! Getting such nice positive feedback is really encouraging :) I personally like green-tea with chestnut cream(*^ v ^*)

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Written: 9:17am, 11 JunAuthor has: 6361 points and 23 badges

i appreciate that you put so much effort into this!love it!

 Written: 11:48am, 11 JunReply written by question author
 

Thank you :)

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Written: 3:09pm, 11 JunAuthor has: 4522 points and 21 badges

Best question yet. 5/5 

 Written: 4:11pm, 11 JunReply written by question author
 

Thank you so much!! It really makes me get more engaged in Peerwise!! :D

 Written: 4:32pm, 12 JunAuthor has: 3871 points and 18 badges
 

That was really, really good...............

 Written: 8:09pm, 12 JunReply written by question author
 

Thank you so much!! :)

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Written: 7:08pm, 11 JunAuthor has: 2959 points and 20 badges

I love this question. I got it wrong because i forgot about the overlap but overall, learned something new. Great Job with the question and the explanation. 

 Written: 7:45pm, 11 JunReply written by question author
 

Thank you :) I am glad you were able to learn something new from my question :D Good luck next time!!

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Written: 5:05pm, 14 JunAuthor has: 2419 points and 16 badges

Wow! Great question. You really put a lot of work in to this and it shows :D

 Written: 5:20pm, 14 JunReply written by question author
 

Thank you :D

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Written: 12:04am, 17 JunAuthor has: 954 points and 15 badges

Jared, you are my hero.

 Written: 8:36am, 17 JunReply written by question author
 

Awwww, thank you!! :) Jared is always here to save the day ;)

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Written: 10:39pm, 18 JunAuthor has: 3679 points and 21 badges

Dear JaredTheHero: I have finally found your AWESOME question about Macaroons :)

I would love to get the Green Tea with Chestnut cream (It sounds like an interesting mix)

 

P.S. - #IAPPROVE. & #YourCLineBuddy :)

 Written: 10:48pm, 18 JunReply written by question author
 

Awwww, thank you so much :D

Green-tea and chestnut tastes really great together ;)

 Written: 10:59pm, 18 JunAuthor has: 3679 points and 21 badges
 

You're welcome~! :)

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