Checking Binomial Distribution Conditions and Calculating Probability
A factory produces light bulbs, and the probability that any given bulb is defective is 0.02. In a sample of 50 bulbs, verify whether this situation can be modeled using a binomial distribution. Justify your answer by checking all necessary conditions. If it can be modeled, calculate the probability that exactly one bulb is defective.
Part a
Given \(X \sim B(n=10, p=0.3)\), calculate \(P(X=2)+P(X=3)\) using the formula \(P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\).
Part a
Using a binomial distribution model, calculate the probability of obtaining exactly 4 successes in 10 trials when the probability of success on each trial is 0.3.