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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.

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%) |

The following explanation has been provided relating to this question:

The following topics have been indicated as being relevant 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*clapWith 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 Aa) Jared wants the macaron to have

some sort of berries flavourin it (either with theorstrawberry flavoured shellsormixed berries cream).bothJared 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 shellsand 62 macarons withmixed berries cream.There are 38 macarons with both

strawberry flavoured shells and mixed berries cream(This is the overlap).if you chose

Option BorOption C, you might have forgotten about the overlap ofstrawberry flavoured shells and mixed berries cream.Part Bb) Jared is happy with anything as long as the macaron

does nothave.buttercreamThe 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, ormixed 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 fillingwhich 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 Cc) Jared is fine with

anything other thanthe combinations ofwith any creamgreen-tea flavoured shellsexcept.chestnut creamJared is fine with any macaron as long as the shells are either

vanilla flavouredorstrawberry 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 withgreen-tea flavoured shells.The highlighted area bellow shows macarons Jared will be happy with.

There are 96 macarons with

vanilla flavouredshellsand 104 macarons withstrawberry 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 gettinggreen-tea flavoured shells with chestnut cream.Part Dd) Jared is fussy and

onlywantswithvanilla flavoured shells.chocolate fudgeThis is fairly straight forward. Jared only wants to have

vanilla flavoured shells with chocolate fudge fillingand 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 CorOption E, you have misinterpreted the question and thought Jared wants any macaron as long as it hasvanilla flavoured shellsorchocolate 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 :)