Question

A manufacturing company makes multi-media software that includes video disk players (VDP) and audio disk players (ADP). It is observed that during the manufacturing, 3 out of 5000 VDPs may be defective and 2 out of 1000 ADPs may be defective.

The company is concerned that the final software should not have any defective parts. What is the probability that the software would not be defective?
a. 1
b. 0.9998
c. 0.999
d. 0.9974

Answer 1

Can anyone help me? Math is my worst subject.

Answer 2

Let \(\text{P(A)}\) be the probability for a defect in VDP and \(\text{P(B)}\) be the probability for a defect in ADP.
\(\text{P(A)}=\frac{3}{5000}=0.0006\)
\(\text{P(B)}=\frac{2}{1000}=0.002\)
∴
To find the probability the software has no effect, you must find \(P(A'⋂B')\)
Considering that the two events are independent,
\(P(A'⋂B')=P(A')P(B')\)

Recall that \(P(X')=1-P(X)\)
\(∴\)
\(P(A')=1-0.006\)
\(P(B')=1-0.002\)
\(P(A'⋂B')=(1-0.0006)(1-0.002)\)

Calculate that and you'll get your answer.