Let a 52 deck of numbered cards be created as follows:
2 special cards: 0 and 1
25 powers of 2: 2, 4, 8, ..., 2^25
25 powers of 3: 3, 9, 27, ..., 3^25
Shuffle the deck and draw at random 3 cards. Evaluate the product of the 3 numbers, say P.
What is the probability of P=0?
What is the probability of P being a non zero integer square?
What is the probability of P being a 4-digit number?
The three probabilities are:
probability of P=0: 0.057692307692307696 which is 3/52
non zero integer square: 0.28022624434389143
a 4-digit number: 0.006470588235294118
The 3 numerators are 1275, 6193, 143 respectively
Each denominator is: comb(52,3) = 22100
def isSquare(n):
""" Input an integer, Returns True iff it is a perfect square. """
if round(n**0.5)**2 == n:
return True
else:
return False
c2s = [2**i for i in range(26)]
c3s = [3**i for i in range(1,26)]
cards = sorted([0]+c2s+c3s)
from itertools import combinations
zeros = 0
squares = 0
fourdigs = 0
count = 0
for comb in combinations(cards,3):
p = comb[0] * comb[1] * comb[2]
count += 1
if p == 0:
zeros += 1
else:
if isSquare(p):
squares += 1
if len(str(p)) == 4:
fourdigs += 1
print(zeros/count, squares/count, fourdigs/count)
print(zeros, squares, fourdigs)
Output:
0.057692307692307696 0.28022624434389143 0.006470588235294118
1275 6193 143
Edited on March 29, 2023, 9:06 am
|
|
Posted by Larry
on 2023-03-29 09:01:20 |
Computer solution
