Six Sigma Green Belt Certification 2025 – 400 Free Practice Questions to Pass the Exam

Question: 1 / 400

A sample of 20 plastic bags is randomly taken from a continuous process. If 15% contain defects, what is the probability of finding two defective bags?

77.06%

85.00%

15.00%

22.94%

To determine the probability of finding exactly two defective bags in a sample of 20 bags, we can use the binomial probability formula. This situation is a classic case where each bag has two possible outcomes: defective or not defective.

In this case, the probability of finding a defective bag (success) is 15%, or 0.15, while the probability of finding a non-defective bag (failure) is 85%, or 0.85.

Using the binomial probability formula:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

where:

- \( n \) is the number of trials (20 bags),

- \( k \) is the number of successes we are interested in (2 defective bags),

- \( p \) is the probability of success (0.15).

Substituting the values:

\[ P(X = 2) = \binom{20}{2} (0.15)^2 (0.85)^{18} \]

Calculating each component:

- \( \binom{20}{2} = \frac{20!}{2!(20-2)!} = 190 \

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