Question

A shipment of inexpensive digital​ watches, including 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?.

Answer 1

0.8926 percent of the time, the shipment will be rejected.

What is Probability?

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.

According to the given information:

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:

$P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}$

The random variable x should stand in for the quantity of defective watches.

The chance that the delivery will be refused is:

$\begin{aligned}&P(x \geq 1)=1-P(0) \\&=1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}\end{aligned}$

= 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:

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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