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

Answer:

6/25

Step-by-step 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

$p(A|B)=\frac{p(A\cap B)}{p(B)}$

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:

$p(A\cap B)=\frac{c}{n}=\frac{6}{800}$ is the probability that the camera has both lens and charging defect

$p(B)=\frac{b}{n}=\frac{25}{800}$ is the probability that the camera has a charging defect

So the conditional probability is

$p(A|B)=\frac{6/100}{25/100}=\frac{6}{25}$