Question

A shipping container contains seven complex electronic systems. Unknown to the purchaser, two are defective. Two of the seven are selected for thorough testing and are then classified as defective or non defective. What is the probability that no defectives are found?

Answer 1

Answer:

     $\large\boxed{\large\boxed{10/21}}$

Explanation:

There are only two mutually exclusive possibilities for each complex electronic system: being defective or being not defective:

• Number of complex electronic systems: 7
• Nmber of defective systems: 2
• Number of not defective systems: 5

Probability that no defective systems are found in the sample is the equal to the probability of selecting them consecutively without replacement and finding each one is not defective:

• Porbability the first is not defective × probability the second is not defective

• 5/7 × 4/6 = 20/42 = 10/21