If you bet on "red" at roulette, you have chance 18/38 of winning. Suppose you make a sequence of independent bets on “red” at roulette, with the decision that you will stop playing once you have won 5 times. What is the chance that after 15 bets you are still playing?
We use binomial probability mass function. To calculate the probability, you have to estimate the probability of having up to 4 successful bets after the 15th. So the final probability will be the sum of the probability to get 0 successful bets in 15 bets, plus the probability to get 1 successful bet, ..., to the probability of having 4 successful bets in 15 bets.
To achieve it:
import scipy.stats as ss
n = 15 # Number of total bets
p = 18./38 # Probability of getting "red" at the roulette
max_sbets = 4 # Maximum number of successful bets
hh = ss.binom(n, p)
total_p = 0
for k in range(1, max_sbets + 1): # DO NOT FORGET THAT THE LAST INDEX IS NOT USED
total_p += hh.pmf(k)
The total probability is now in total_p.