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We can use Bayes' Theorem to estimate the probability of someone not having an effect (meaning they get infected after vaccination) for both Covishield and Covaxin, considering a population of 1.4 billion individuals. Assumptions: We assume equal distribution of both vaccines in the population (700 million each). We focus on individual protection probabilities, not overall disease prevalence. Calculations: Covishield: Prior Probability (P(Effect)): Assume 10% of the vaccinated population gets infected (no effect), making P(Effect) = 0.1. Likelihood (P(No Effect|Effect)): This represents the probability of someone not being infected given they received Covishield. Given its 90% effectiveness, P(No Effect|Effect) = 0.9. Marginal Probability (P(No Effect)): This needs calculation, considering both vaccinated and unvaccinated scenarios. P(No Effect) = P(No Effect|Vaccinated) * P(Vaccinated) + P(No Effect|Unvaccinated) * P(Unvaccinated) Assuming 50% effectiveness for unvaccinated indivi...

  Integrating C/C++ libraries into Python applications can be beneficial in various scenarios: 1. Performance Optimization:    - C/C++ code often executes faster than Python due to its lower-level nature.    - Critical sections of code that require high performance, such as numerical computations or data processing, can be implemented in C/C++ for improved speed. 2. Existing Libraries:    - Reuse existing C/C++ libraries that are well-established, optimized, and tested.    - Many powerful and specialized libraries in fields like scientific computing, machine learning, or image processing are originally written in C/C++. Integrating them into Python allows you to leverage their functionality without rewriting everything in Python. 3. Legacy Code Integration:    - If you have legacy C/C++ code that is still valuable, integrating it into a Python application allows you to modernize your software while preserving existing functionality...