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### Step-by-step

**Step 1/1**

- P(X = k) is the probability of getting k successes (in this case, bulbs that last at least 100 hours) in n trials (20 bulbs).
- C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient).
- p is the probability of success in each trial (0.95, as the supplier promises a 95% reliability).
- (1 - p) is the probability of failure in each trial (0.05)The Probability Of A Shipment Passing The Test Assignment Paper.

**Therefore, the probability of passing the test is 0.000025606 or 0.00256%**.

- 1 represents the number of failures that would cause the batch to fail (i.e., 2 or more bulbs going out).
- 20 is the number of trials (i.e., the number of bulbs tested).
- 0.95 is the probability of success in each trial (i.e., the 95% reliability promised by the supplier).
- TRUE indicates that the function should return the cumulative distribution function (i.e., the probability of having 1 or fewer failures).

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