Kata

We have got a gun that shoots little balls of painting of different colours. We want to calculate the probability in having a certain number of shots with certain colours in a specific order.

Before start shooting, the balls are mixed in such way that each ball has the same probabilty of being selected to be shot. This action is repeated after each shot.

For example the gun will be feed with a total of 18 balls: 9 yellow, 4 red and 5 blue. Like the sets we have below.

We want to know the probabilty for this set of balls (balls_set) in having the following event that has 4 consecutive shots: e1 = ["RD", "YL", "YL", "BL"].

RD means Red, YL means Yellow and BL means Blue

The probability will be:

p(e1) = 4/18 * 9/17 * 8/16 * 5/15 = 1440/73440 = 1/51

But the following event, for the same balls_set, is impossible for this event of 5 shots: e2 = ["RD", "YL", "YL", "BL", "GN"] p(e2) = 0. The new one here is GN, GN means green. There are no green balls in the set given above.

You will be given an unordered set of balls with different colours and a desired event. The balls_set has full words for the names of the colours (first letter in Capital letters) as an array. The event is an array, too, but has the corresponding abbreviation for the color. (see the table bellow). You should output the probability of the desired event as a non-reducible fraction with its numerator and denominator in an array, [num, den] (num and den should be co-primes).

The examples given above will be:

set_balls = ["Red","Red","Blue","Yellow","Yellow","Yellow","Red", "Yellow","Yellow","Blue","Yellow","Red","Blue","Yellow","Blue","Yellow","Blue",Yellow"]
e = ["RD", "YL", "YL", "BL"]
find_prob(set_balls, e1) === [1,51]

And the above case when the probability is 0, the function will output an array with the word "Impossible" in it.

set_balls = ["Red","Red","Blue","Yellow","Yellow","Yellow","Red", "Yellow","Yellow","Blue","Yellow","Red","Blue","Yellow","Blue","Yellow","Blue",Yellow"]
e = ["RD", "YL", "YL", "BL,"GN"]
find_prob(set_balls, e1) === ['Impossible']

You sould have in mind that events with very low probability very close to 0 are improbable, but events with probability equals to 0 are impossible The following table shows the correspondent abreviations with all the possible colours of balls that are available for this kata.

Abbreviation        Color 
AL                  Aluminum 
AM                  Amber 
BG                  Beige 
BK                  Black 
BL                  Blue 
BN                  Brown 
BZ                  Bronze 
CH                  Charcoal 
CL                  Clear 
GD                  Gold 
GN                  Green 
GY                  Gray 
GT                  Granite 
IV                  Ivory 
LT                  Light  
OL                  Olive 
OP                  Opaque 
OR                  Orange 
PK                  Pink 
RD                  Red 
SM                  Smoke 
TL                  Translucent 
TN                  Tan 
TP                  Transparent 
VT                  Violet 
WT                  White 
YL                  Yellow 

The dictionary ABBREVIATIONS (in Ruby $ABBREVIATIONS) has been preloaded for you to speed up the creation of your solution.

Features of the Random Tests:

length of balls_set (total amount of balls) between 20 and 100000
amount of events according to the amount of total balls

More cases in the example tests.

The gun has a huge deposit to charge incredible amount of painting balls.

Enjoy it!