Question

A shipment of 70 laptops, including 6 that are defective, is sent to a retail store. The receiving department selects 9 at random for testing and rejects the whole shipment if 1 or more in the sample are found to be defective. What is the probability that the shipment will be rejected?

Answer 1

To calculate the probability that the shipment will be rejected, we need to consider the number of vays the sample can contain at least one lefective laptop.
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Let's break down the calculation step by step:
Step 1: Determine the total number of possible samples of 9 laptops selected from the shipment of 70 laptops. This can be calculated using combinations:
Total number of possible samples = C(70, 9) =
70!1 (9!* (70-9)!) ~ 138,355,710
Step 2: Determine the number of samples that contain at least one defective laptop. We have 6 defective laptops out of the total 70 laptops in the shipment. We can calculate the number of samples with at least one defective laptop using complementary probability:
Number of samples with at least one defective
laptop = Total number of samples - Number of
samples with no defective laptops
To find the number of samples with no defective laptops, we select 9 laptops out of the 64 non-defective laptops:
Number of samples with no defective laptops =
C(64, 9) = 64!/ (9! * (64-9)!) ~ 2,279,232
Therefore. the number of sambles with at least

Answer 2

To calculate the probability that the shipment will be rejected, we need to consider the number of ways the sample can contain at least one defective laptop.

Let's break down the calculation step by step:

Step 1: Determine the total number of possible samples of 9 laptops selected from the shipment of 70 laptops. This can be calculated using combinations:

Total number of possible samples = C(70, 9) = 70! / (9! * (70-9)!) ≈ 138,355,710

Step 2: Determine the number of samples that contain at least one defective laptop. We have 6 defective laptops out of the total 70 laptops in the shipment. We can calculate the number of samples with at least one defective laptop using complementary probability:

Number of samples with at least one defective laptop = Total number of samples - Number of samples with no defective laptops

To find the number of samples with no defective laptops, we select 9 laptops out of the 64 non-defective laptops:

Number of samples with no defective laptops = C(64, 9) = 64! / (9! * (64-9)!) ≈ 2,279,232

Therefore, the number of samples with at least one defective laptop = Total number of samples - Number of samples with no defective laptops
≈ 138,355,710 - 2,279,232
≈ 136,076,478

Step 3: Calculate the probability that the shipment will be rejected by dividing the number of samples with at least one defective laptop by the total number of possible samples:

Probability of shipment rejection = Number of samples with at least one defective laptop / Total number of possible samples
≈ 136,076,478 / 138,355,710
≈ 0.9829

Therefore, the probability that the shipment will be rejected is approximately 0.9829 or 98.29%.