Question

1. in a batch of 200 products, 5 are defective. what is the theoretical probability of selecting a non - defective item?

a. 0.975
b. 0.02
c. 0.95
d. 0.05

Explanation:

Step1: Calculate the number of non - defective items

The total number of products is \(n = 200\), and the number of defective items is \(d=5\). So the number of non - defective items \(n_{nd}=200 - 5=195\).

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the event \(A\) is selecting a non - defective item. So \(P=\frac{n_{nd}}{n}\). Substitute \(n_{nd} = 195\) and \(n = 200\) into the formula: \(P=\frac{195}{200}=\frac{195\div5}{200\div5}=\frac{39}{40}=0.975\).

Answer:

A. 0.975