Conditional Probability

Suppose you draw a card from a deck of 52 cards and it’s red. What is the probability that it is also a diamond ?

Suppose you draw a card from a deck of 52 cards and it’s red. What is the probability that it is a queen ?

Suppose you draw a card from a deck of 52 cards and it’s red. What is the probability that it is a queen of diamonds ?

import random

suits  = ["diamonds", "clubs", "spades", "hearts"]
reds   = ["diamonds", "hearts"]
blacks = ["clubs", "spades"]
cards  = ["1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "J", "Q", "K"]

print ("Number of cards in the deck:", len(suits)*len(cards))

Number of cards in the deck: 52

# initialize couters
c_draws   = 0
c_reds    = 0
c_reds_and_diamonds = 0
c_reds_and_queens   = 0
c_queens_and_diamonds_and_red = 0

# draw the cards at random 
n_draws = 1000000
for i in range(1, n_draws):   
    
    c_draws += 1
    s = random.choice(suits)
    c = random.choice(cards)
    # print (s, c)    
    
    # select the cards
    if s in reds:
        c_reds += 1

        if s  == "diamonds":
            c_reds_and_diamonds += 1
        
        if c == "Q":
            c_reds_and_queens += 1
            
        if s  == "diamonds" and c == "Q":
            c_queens_and_diamonds_and_red += 1

print ("Total number of draws                 = ", c_draws)
print ("Total number of diamonds              = ", c_reds)
print ("Total number of diamons queens        = ", c_reds_and_diamonds)
print ("Total number of red queens            = ", c_reds_and_queens)
print ("Total number of red queens of diamons = ", c_queens_and_diamonds_and_red)

Total number of draws                 =  999999
Total number of diamonds              =  500808
Total number of diamons queens        =  250313
Total number of red queens            =  38687
Total number of red queens of diamons =  19274

print ("""Suppose you draw a card from a deck of 52 cards and it’s red.\nWhat is the probability that it is also a diamond ?""")

print ("Frequency                = ", round(c_reds_and_diamonds/float(c_reds),3))

Suppose you draw a card from a deck of 52 cards and it’s red.
What is the probability that it is also a diamond ?
Frequency                =  0.5

print ("Suppose you draw a card from a deck of 52 cards and it’s red.\nWhat is the probability that it is a queen ?")
print ("Frequency                = ", round(c_reds_and_queens/float(c_reds),3))

Suppose you draw a card from a deck of 52 cards and it’s red.
What is the probability that it is a queen ?
Frequency                =  0.077

print("Suppose you draw a card from a deck of 52 cards and it’s red.\nWhat is the probability that it is a queen of diamonds ?")
print ("Frequency                = ", round(c_queens_and_diamonds_and_red/float(c_reds),3))

Suppose you draw a card from a deck of 52 cards and it’s red.
What is the probability that it is a queen of diamonds ?
Frequency                =  0.038