How to find probability in repeated trials?

  • Thread starter TiredEngineer
  • Start date
  • Tags
    Probability
In summary, the individual is trying to determine the number of units they need to test in order to have a 0.85 probability of finding at least one defective product, given a 0.05 defect rate. They attempted to solve this using the binomial probability formula, but found it difficult and were unsure if it was the correct approach. However, it was pointed out that they should find it easier to solve for the probability of having no failures and then subtracting that from 1.
  • #1
TiredEngineer
2
0
Info: I made the mistake of starting engineering grad school years after finishing my undergrad, and forgot my basic prob/stat. This is related to reliability engineering.

Homework Statement



How many arbitrarily selected units do I have to test so that my probability is 0.85 of finding one at least one defective product if I have a 0.05 defect rate for this particular product.

Homework Equations



Binomial Probability Formula

binomial%20probability%20formula.gif


The Attempt at a Solution



I tried setting the formula to be equal to 0.85, k=1 (because I only need one to fail), and left number of trials as "n" to solve for. I have tried to solve for this and was having a tough time, and I am not even sure if this is the correct approach.

Edit: p=0.05 and q=1-p=0.95
 
Last edited:
Physics news on Phys.org
  • #2
TiredEngineer said:
Info: I made the mistake of starting engineering grad school years after finishing my undergrad, and forgot my basic prob/stat. This is related to reliability engineering.

Homework Statement



How many arbitrarily selected units do I have to test so that my probability is 0.85 of finding one at least one defective product if I have a 0.05 defect rate for this particular product.

Homework Equations



Binomial Probability Formula

binomial%20probability%20formula.gif


The Attempt at a Solution



I tried setting the formula to be equal to 0.85, k=1 (because I only need one to fail), and left number of trials as "n" to solve for. I have tried to solve for this and was having a tough time, and I am not even sure if this is the correct approach.

Edit: p=0.05 and q=1-p=0.95

The probability of getting at least one failure after k trials is one minus the probability of getting no failures after k trials. You should find the 'no failures' case easier to solve.
 
  • #3
What Dick said. To elaborate, setting k=1 gives the probability of exactly one failure - you want at least one.
 
  • #4
What Dick said. To elaborate, setting k=1 gives the probability of exactly one failure - you want at least one.
 
  • #5
Thanks for the help guys. That was a herp-derp moment for me.
 

1. What is probability in repeated trials?

Probability in repeated trials refers to the likelihood of a specific outcome occurring after multiple trials of the same experiment or event. It is based on the concept that the more trials are conducted, the more accurate the probability of a certain outcome becomes.

2. How do you calculate probability in repeated trials?

To calculate probability in repeated trials, you need to divide the number of times the specific outcome occurred by the total number of trials conducted. For example, if you flip a coin 10 times and it lands on heads 5 times, the probability of getting heads is 5/10 or 0.5.

3. What is the difference between theoretical and experimental probability in repeated trials?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. On the other hand, experimental probability is based on actual data collected from repeated trials and may vary from the theoretical probability due to chance or other factors.

4. How does the law of large numbers relate to probability in repeated trials?

The law of large numbers states that as the number of trials increases, the experimental probability will approach the theoretical probability. In other words, the more trials you conduct, the closer your results will be to the expected probability.

5. Can probability in repeated trials be applied to real-life situations?

Yes, probability in repeated trials can be applied to many real-life situations, such as predicting the likelihood of winning a game, the chances of a stock market investment being profitable, or the probability of a medical treatment being successful based on previous trials. It is a useful tool for making informed decisions and understanding the likelihood of certain outcomes.

Similar threads

Probability of Hypokalemia w/ 1 or Multiple Measurements
    • Calculus and Beyond Homework Help
Replies
4
Views
843
Calculating Overbooking Probability for a Plane with Independent Passengers
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
B Decision for conditional probability instead of intersection of events
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
807
Probability and Bernoulli trials
    • Calculus and Beyond Homework Help
Replies
9
Views
4K
A combinatorial probability question
    • Precalculus Mathematics Homework Help
Replies
18
Views
455
Mixed random variables problem
    • Calculus and Beyond Homework Help
Replies
6
Views
845
Bernoulli and Bayesian probabilities
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Why isn't this a binomial distribution?
    • Calculus and Beyond Homework Help
Replies
13
Views
1K
If duelist A shoots first, what is the probability A wins?
    • Calculus and Beyond Homework Help
Replies
14
Views
2K
Finding Probability Density Functions for Independent Random Variables
    • Calculus and Beyond Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top