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This question has been answered by 22 people and has an average rating of 3.95 (based on 19 ratings)
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.
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
| 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
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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.
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.
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.
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.
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 :)