0.8926 percent of the time, the shipment will be rejected.
<h3>What is Probability?</h3>
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
<h3>According to the given information:</h3>
A delivery of 50 cheap digital watches, 10 of which are flawed.
A digital watch's likelihood of malfunctioning
P = 10/50
= 0.2
Size of sample: n = 10
Additionally, if they find one or more samples to be defective, they reject the entire cargo.
Making use of the binomial probability formula:
![P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28x%29%3D%7B%20%7D%5E%7Bn%7D%20C_%7Bx%7D%20p%5E%7Bx%7D%281-p%29%5E%7Bn-x%7D)
The random variable x should stand in for the quantity of defective watches.
The chance that the delivery will be refused is:
![\begin{aligned}&P(x \geq 1)=1-P(0) \\&=1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26P%28x%20%5Cgeq%201%29%3D1-P%280%29%20%5C%5C%26%3D1-%7B%20%7D%5E%7B10%7D%20C_%7B0%7D%280.2%29%5E%7B0%7D%280.8%29%5E%7B10%7D%5Cend%7Baligned%7D)
= 1 - (0.8)
= 0.8926
As a result, 0.8926 percent of the time, the shipment will be rejected.
To know more about binomial probability visit:
brainly.com/question/13072083
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I understand that the question you are looking for is:
A shipment of 50 inexpensive digital watches, including 10 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected