I have 200 candies in an hourglass dispenser. There are 40 each of red, white, blue, yellow and green. Each time I turn the hourglass over the candies get thoroughly mixed and 20 candies are poured into a cup. I like the blue candies best.
When I want candy, I turn over the dispenser and sort through the candies in the cup. I leave all of the blue ones in the cup and put the rest back. Then I turn over the hourglass a second time. The dispenser fills the cup so that I get exactly 20 candies, which I eat. I continue this way until the dispenser is empty.
How many blue candies will be in the final cupful?
Note:The dispenser dispense just the right amount so that to total will still be 20; so if 4 blues remain, it will dispense 16.
This is a simulation, not an exact calculation
Counting the number of blue candies per each of the 20 batches, after 10,000 trials:
[6.9392, 6.3839, 5.785, 5.2228, 4.5325, 3.8313, 3.0977, 2.2976, 1.4219, 0.4881]
So that the requested final cupful has an expected number of slightly less than 1/2 blue candy.
-------------
import random
candies = list('R'*40 + 'W'*40 + 'Y'*40 + 'B'*40 + 'G'*40)
random.shuffle(candies)
blue_list = [0 for n in range(10)]
big = 10000
for reps in range(big):
random.shuffle(candies)
remains = candies
for n in range(10):
random.shuffle(remains)
if n < 9:
dispensed = remains[:20]
remains = remains[20:]
tobereturned = []
for d in dispensed:
if d != 'B':
tobereturned.append(d)
returnee_number = len(tobereturned)
dispensed = ['B']*(20 - returnee_number)
remains = remains + tobereturned
random.shuffle(remains)
dispensed = dispensed + remains[:returnee_number]
remains = remains[returnee_number:]
blue_list[n] += dispensed.count('B')
else:
dispensed = remains
blue_list[n] += dispensed.count('B')
blues_per_batch = []
for b in blue_list:
blues_per_batch.append(b/big)
print(blues_per_batch)
|
|
Posted by Larry
on 2023-12-12 14:14:14 |
Simulation
