Discrete probability

In summary: P(E)=C(90,10)*C(100,3)/C(100,4) In summary, the probability of obtaining exactly one defective microprocessor is 10/100.
  • #1
Townsend
232
0
There is a question in my text that list an answer in the back of the book that seems wrong to me.
It is,

"Four microprocessors are randomly selected from a lot of 100 microprocessors among which 10 are defective. Find the probability of obtaining no defective microprocessors."

There are C(100,4) ways of selecting 4 microprocessors from 100 and this is our sample space. There are 90 non-defective microprocessors and so there are C(90,4) ways to select a non-defective microprocessor. So our number of out comes of the event is C(90,4) and so the probability of the event is

P(E)=C(90,4)/C(100,4).

The answer in the back of the textbook is given as

C(90,10)/C(100,10)

This answer does not make much sense to me since we are selecting 4 things and not 10 things. Am I right or is the book right?

Thanks
 
Physics news on Phys.org
  • #2
The book is incorrect; you are not.
 
  • #3
Thanks Gokul...

I have another quick question,

"Four microprocessors are randomly selected from a lot of 100 microprocessors among which 10 are defective. Find the probability of obtaining exactly one defective microprocessor"

The sample space is C(100,4) but the outcomes of the event are a bit different. Here there are C(90,4) ways to get all good processors but we want exactly one bad one in our 4. Well the other 3 must be good so they are C(90,3) ways for that to happen and there are C(10,1) ways to get one bad processor. So I am thinking that the ways to get the good processors plus the ways to get the bad processor make up the total number of ways to get exactly one bad processor. So

P(E)=(C(10,1)+C(90,3))/C(100,4)

is the probability of obtaining exactly one bad microprocessor.

Thanks
 
  • #4
Townsend said:
Thanks Gokul...

I have another quick question,

"Four microprocessors are randomly selected from a lot of 100 microprocessors among which 10 are defective. Find the probability of obtaining exactly one defective microprocessor"

The sample space is C(100,4) but the outcomes of the event are a bit different. Here there are C(90,4) ways to get all good processors but we want exactly one bad one in our 4. Well the other 3 must be good so they are C(90,3) ways for that to happen and there are C(10,1) ways to get one bad processor. So I am thinking that the ways to get the good processors plus the ways to get the bad processor make up the total number of ways to get exactly one bad processor. So

P(E)=(C(10,1)+C(90,3))/C(100,4)

is the probability of obtaining exactly one bad microprocessor.

Thanks

You have to get 1 bad AND 3 good... so you have to multiply:
P(E)=(C(10,1)*C(90,3))/C(100,4)
 
  • #5
Yes, these are not mutually exclusive events. They are independent, sequential events.

There are 10 ways of picking the defect. For each of these 10 choices, there are C(90,3) ways of picking the 3 good ones. So the "total" here will be the product.
 

What is discrete probability?

Discrete probability is a branch of mathematics that deals with the study of events that have a finite or countable number of possible outcomes. It involves calculating the likelihood of these outcomes occurring based on certain conditions or variables.

How is discrete probability different from continuous probability?

Discrete probability deals with events that have a finite or countable number of possible outcomes, while continuous probability deals with events that have an infinite number of possible outcomes. Discrete probability also involves calculating probabilities using a probability mass function, while continuous probability uses a probability density function.

What are some common examples of events that can be modeled using discrete probability?

Some common examples include flipping a coin, rolling a die, drawing cards from a deck, and counting the number of occurrences of an event in a sample space. Discrete probability can also be used in fields such as genetics, economics, and computer science.

How is probability calculated in discrete probability?

In discrete probability, the probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented using a probability distribution or a probability mass function.

What are some techniques for solving problems involving discrete probability?

Some common techniques include using the fundamental principle of counting, using probability rules such as the addition and multiplication rules, and using probability distributions and tables. Other techniques include using tree diagrams, Venn diagrams, and Bayes' theorem.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
10K
  • Introductory Physics Homework Help
Replies
1
Views
496
  • Introductory Physics Homework Help
Replies
2
Views
492
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
469
  • Precalculus Mathematics Homework Help
Replies
7
Views
4K
Replies
12
Views
672
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
739
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Back
Top