A shipment of 20 cameras includes 3 that are defective. What is the minimum number of cameras that must be selected if we require that P(at least 1 defective) ≥ .8?
Step 1 of 1:
In this question, we need to find the minimum number of cameras that must be selected if we require that
We can write above probability like this,
Let is defined as a number of defective cameras.
Here, random variable follows a hypergeometric distribution, because we are selecting cameras from twenty cameras of which some are defectives and some are non-defectives.
A random variable is said to have a hypergeometric probability distribution if and only if
Where is an integer subject to the restrictions and
Hence we can find the value of by substituting the value of r from 4 to 8 into equation (1), and we will check the value of probability whether it is equal to 0.2 or not. Then we can conclude the minimum number of cameras .
i). If ,
ii). If ,
iii). If ,
iii). If ,
iv). If ,
Both the probability value of equation (1) and (3) are approximately equal.
Hence is the minimum number that the probability .