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The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects, 25 cameras had charging defects, and 6 cameras had both defects. What is the probability that a camera has a lens defect given that it has a charging defect?

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Answer:

0.025

Step-by-step explanation:

-This is a conditional probability problem.

-Let L denote lens defect and C charging defect.

#We first calculate the probability of a camera having a lens defect;

[tex]P(lens)=\frac{Lens}{Total}\\\\=\frac{20}{800}\\\\=0.025[/tex]

#Calculate the probability of a camera having a charging defect:

[tex]P(Charging)=\frac{Charging}{Total}\\\\=\frac{25}{800}\\\\=0.03125[/tex]

The  the probability that a camera has a lens defect given that it has a charging defect is calculated as:

[tex]P(L|C)=\frac{P(C)P(L)}{P(C)}\\\\=\frac{0.025\times 0.03125}{0.03125}\\\\=0.025[/tex]

Hence,  the probability that a camera has a lens defect given that it has a charging defect is 0.025