Conditional Probability Question

In summary, the conversation was about calculating the probability that both televisions in a shipment of 100, where 6 are defective, are defective. While one person thought the answer was 5/99, it was corrected that the correct answer is 1/330. This is because the probability of both being defective is the probability of the first being defective (6/100) multiplied by the probability of the second being defective given that the first is defective (5/99). In conclusion, the probability of both televisions being defective is indeed 1/330.
  • #1
faisy_master
2
0

Homework Statement



In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective?

Homework Equations



the Answer is somewhat weird! it says it is 1/330 ! which is really beyond by recognition

The Attempt at a Solution



What I think is that it is 5/99!

The first defective TV would have probability of 6/100 ... but the second defective TV would have probability as 5/99 BECAUSE one is reduced from the defective TV Set and one is also reduced from the sample size.

What do you think?
 
Last edited:
Physics news on Phys.org
  • #2
You are answering the wrong question! Yes, the probability that the second set is also defective is 5/99. But the question asked is "what is the probability that both are defective?"

In order that they both be defective, the first has to already be defective and the probability of that is, as you say, 6/100. The probability that the first is defective and the second is defective is (6/100)(5/99)= (3/50)(5/99)= (1/10)(1/33)= 1/330.

The probability of A and B is (Probability of A) times (Probability of B given A).
Your answer, 5/99, is "Probability of B given A" but you still need to multiply by "Probability of A".
 
  • #3
wow !

thanks ... you are the best !


one last thing ... does it mean that I am not a complete retard ? :redface:

:)
 

1. What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted by P(A|B), where A is the event of interest and B is the event that has already occurred.

2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of the two events (P(A∩B)) by the probability of the event that has already occurred (P(B)). This can be written as P(A|B) = P(A∩B)/P(B).

3. What is the difference between conditional probability and regular probability?

The main difference between conditional probability and regular probability is that conditional probability takes into account the occurrence of a specific event, while regular probability does not consider any previous events. Conditional probability is based on a subset of the total sample space, while regular probability considers the entire sample space.

4. What are some real-life examples of conditional probability?

Some real-life examples of conditional probability include: the probability of getting a job offer given that you have a college degree, the probability of a patient having a specific disease given that they have certain symptoms, and the probability of a sporting event outcome given the weather conditions.

5. How is conditional probability used in data analysis?

Conditional probability is commonly used in data analysis to understand the relationship between two events and to make predictions based on previous data. It is also used in statistical modeling to identify patterns and correlations between variables. Additionally, conditional probability is used in machine learning to train algorithms and make predictions based on conditional relationships.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
7
Views
4K
  • Precalculus Mathematics Homework Help
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
771
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
997
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
3K
Back
Top