Solution
To estimate the minimum number of balls that should be in the container, we need to consider the probability of drawing two red balls given the total number of balls in the container. Since balls are drawn without replacement therefore probability of two red balls can be given as
\begin{align}
P(RR) = \frac{n_{r}}{n_r + n_b} * \frac{n_r - 1}{ n_r + n_b - 1}
\end{align}
Since we want to have estimate minimum number of total balls , therefor we can keep number of black balls = 1 ,
incrementally increase the number of red balls until the probability of drawing two red balls is >= 1/2.
def probability_two_reds(num_red, num_black):
"""
Calculate the probability of drawing two red balls given the number of red balls and total balls.
"""
total_balls = num_red + num_black
return (num_red / total_balls) * ((num_red - 1) / (total_balls - 1))
def estimate_minimum_balls():
num_red = 2 # minimum number of red balls should start from 2 as per given question
num_black = 1
while True:
prob = probability_two_reds(num_red, num_black)
if prob >= 0.5:
return num_red + num_black
num_red += 1
# Estimate the minimum number of balls
min_balls = estimate_minimum_balls()
print("Minimum number of balls in the container:", min_balls)