Determine and use the probabilities 𝑃(𝑋 = 𝑟) = (𝑛 𝑟) 𝑝𝑟 (1 − 𝑝)𝑛−𝑟 associated with the binomial distribution with parameters 𝑛 and 𝑝.

A quality-control inspector tests batches of electronic components. The probability that a randomly selected component is defective is $0.08$. If a batch of 15 components is tested, what is the probability that exactly 3 components are defective?

A quality-control officer inspects batches of light bulbs. Historical data shows that $8\%$ of bulbs produced are defective. If a random sample of $15$ bulbs is selected, determine the probability that exactly $2$ bulbs are defective. Express your answer as a decimal, correct to $4$ decimal places.

A manufacturer produces electronic components, and historical data shows that 15% of components are defective. A quality inspector randomly selects 8 components from the production line. Let \(X\) represent the number of defective components in the sample. What is the probability that exactly 2 components are defective?