🧮 Bernoulli and Binomial Distributions

Probability distribution problem

Calculate the probability of a certain number of successes in independent trials.

Theory:

• Bernoulli Trial: A random experiment with two possible outcomes: success (with probability $p$) and failure (with probability $1-p$).

• Binomial Distribution: The probability of exactly $k$ successes in $n$ independent Bernoulli trials is given by:

$$P(X=k)=C(n,k)p^k(1-p{)}^{n-k}$$

Where:

• $n$: Number of trials
• $k$: Number of successes
• $p$: Probability of success in each trial