Problem 108E

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?

Answer:

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,

…….(1)

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

[

…………..(2)

Where is an integer subject to the restrictions and

Here,

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 ,

……..(3)

Both the probability value of equation (1) and (3) are approximately equal.

Hence is the minimum number that the probability .