Question

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?

Answer 1

6/25

Explanation:

Given two events A and B, the conditional probability of event A is the probability that event A occurs given that event B has occurred. It is calculated as

`p(A|B)=(p(A\cap B))/(p(B))`

where

`p(A\cap B)` is the probability that both A and B occur at the same time

`p(B)` is the probability that B occurs

In this problem, we call:

A = the camera has a lens defect

B = the camera has a charging defect

Here we have:

a = 20 is the number of cameras with lens defects

b = 25 is the number of cameras with charging defects

c = 6 is the number of cameras having both defects

n = 800 is the total number of cameras

So we have:

`p(A\cap B)=(c)/(n)=(6)/(800)` is the probability that the camera has both lens and charging defect

`p(B)=(b)/(n)=(25)/(800)` is the probability that the camera has a charging defect

So the conditional probability is

`p(A|B)=(6/100)/(25/100)=(6)/(25)`