Answer: 0.8926
Step-by-step explanation:
Given : A shipment of 50 inexpensive digital watches, including 10 that are defective.
The probability that a digital watch is defective [tex]: p=\dfrac{10}{50}=0.2[/tex]
Sample size : n=10
Also, they reject the whole shipment if 1 or more in the sample are found defective.
Using the binomial probability formula :
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
Let x be the random variable that represents the number of defective watches.
The probability that the shipment will be rejected :-
[tex]P(x\geq1)=1-P(0)\\\\=1-^{10}C_0(0.2)^0(0.8)^{10}\\\\=1-(0.8)^{10}=0.8926258176\approx0.8926[/tex]
Hence, the probability that the shipment will be rejected = 0.8926
