Calculating Probability of Defective Pens
What is the probability that exactly 2 pens are defective?
The probability that exactly 2 pens, out of a package of 5, from the given company are defective is approximately 7.29%. This is calculated using the binomial probability formula.
Answer:
The company produces pens with a defect probability of 0.1 and we are looking for exactly 2 defective pens out of a package of 5. By applying the binomial probability formula: Pr(2 out of 5) = C(5, 2) * (0.1^2) * ((1-0.1)^(5-2)), we find that the probability of exactly 2 pens being defective out of a 5-pen package from this company is approximately 0.0729, or 7.29%.
Detail Explanation:
It is known that marking pens produced by a certain company will be defective with probability 0.1 independently of each other. The company sells pens in packages of 5. In this scenario, we are interested in finding the probability of exactly 2 pens being defective.
As it is asking about probability, we can utilize the binomial probability formula to solve this problem. The formula is represented as Pr(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where C(n, k) is the number of combinations items taken k at a time, p is the probability of success, n is the total number of items, and k is the total number of successes.
Given that the company has a defect probability of 0.1 and we are interested in exactly 2 defective pens out of 5, we can substitute these values into the formula: Pr(2 out of 5) = C(5, 2) * (0.1^2) * ((1-0.1)^(5-2)). By performing the calculations, we arrive at the probability of 0.0729, or 7.29%.