What are the various probability distributions, give respective formulas of each type of distribution. Now solve the problem“The probability that at least one of the two independent events occurs is 0.5. Probability thatthe first event occurs but not the second is 3/25. Also the probability that the second event occurs but not the first is 8/25.”Find the probability that none of the two events occurs

Probability distributions play a crucial role in statistical analysis by describing the likelihood of different outcomes in a given set of events. There are several probability distributions, each with its own characteristics and use cases. In this context, we'll discuss a few important probability distributions and then solve the provided problem using these concepts.

### Probability Distributions:

1. Binomial Distribution:
   - The binomial distribution is characterized by two parameters: the number of trials (\(n\)) and the probability of success in a single trial (\(p\)).
   - Formula: \(P(X = k) = C(n, k) \cdot p^k \cdot (1-p)^{n-k}\), where \(C(n, k)\) is the binomial coefficient.

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