Small metal springs are packed in boxes of 100 and 0:5 per...

Small metal springs are packed in boxes of 100 and 0:5 per cent of the total output of springs are defective. Determine the probability that any one box chosen at random shall have:
(a) no defective
(b) 2 or more defectives

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Probability Calculation Techniques

Probability calculation involves applying the rules and formulas of probability distributions to determine the likelihood of particular outcomes. In this context, it includes computing probabilities for events such as 'no defective items' or 'two or more defectives', by either directly applying the distribution formulas or using complementary probabilities to simplify the process.

Binomial Distribution

The binomial distribution models the number of successes (or, in quality control, defective items) in a fixed number of independent trials, where each trial has the same probability of success. It is characterized by two parameters: n, the number of trials, and p, the probability of a success in each trial. This distribution is used to calculate the probability of obtaining a specific number of successes using the formula P(X = k) = C(n, k) p^k (1-p)^(n-k).

Poisson Distribution

The Poisson distribution serves as an approximation to the binomial distribution when the number of trials is large and the probability of success is small, such that the product np remains moderate. It is characterized by a single parameter, ? (lambda), which represents the average number of occurrences in a given interval. This approximation simplifies calculations in scenarios involving rare events.

Please give Ace some feedback