Using Basic Counting Formulas?

In summary, there are 75,287,520 samples of size 5 in a set of 100 widgets. When considering the fact that 3 of the widgets are broken, the probability of a set of 5 having no broken widgets is (97*96*95*94*93)/(100*99*98*97*96). To find the number of samples with at least one broken widget, you can use the basic counting formula by subtracting the number of samples of size 5 for a set of 97 widgets from the number of samples for 100 widgets.
  • #1
liahow
6
0
I am working on a problem in which there are 100 widgets. I need to find how many samples of size 5 there are, which I found to be 75,287,520. No problem there. I am not sure how to go about the next part, however. In the original set of 100 widgets, 3 are broken. How many of the samples of 5 contain at least one of these broken widgets? No idea how to do that. Can someone please help? Thanks!
 
Physics news on Phys.org
  • #2
The probability that a given set of 5 widgets has no broken ones is
(97*96*95*94*93)/(100*99*98*97*96). Multiply that by the total number of combinations to get the number without any broken.
 
  • #3
If you want to use the basic counting formula, remove the 3 bad widgets from the set and you have 97. Calculate the number of samples of size 5 for the 97 and subtract from the number of samples of 5 for 100.
 

1. What are the basic counting formulas?

The basic counting formulas are the fundamental principles used to count the number of possible outcomes in a given scenario. These include the multiplication rule, addition rule, and permutation and combination formulas.

2. When should I use the multiplication rule?

The multiplication rule is used when the outcomes of two or more events are independent, meaning the outcome of one event does not affect the outcome of the other events. It is also used when counting the number of ways to arrange objects in a specific order.

3. What is the addition rule used for?

The addition rule is used when the outcomes of two or more events are mutually exclusive, meaning they cannot occur at the same time. It is also used when counting the number of ways to select one or more objects from a larger set.

4. How do I use the permutation formula?

The permutation formula is used when the order of the objects in a set matters. It is used to count the number of ways to arrange a set of objects in a specific order without repetition.

5. When do I use the combination formula?

The combination formula is used when the order of the objects in a set does not matter. It is used to count the number of ways to select a subset of objects without considering their order.

Similar threads

MHB Counting the elements in sets
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
I How far and how close to p=0.05 for statistical significance?
    • Set Theory, Logic, Probability, Statistics
Replies
22
Views
2K
I Unbiasedness of estimates
    • Set Theory, Logic, Probability, Statistics
Replies
9
Views
1K
A Confused about magnitude of error
    • Set Theory, Logic, Probability, Statistics
Replies
18
Views
2K
I Confused about using Monte Carlo for error estimation
    • Set Theory, Logic, Probability, Statistics
Replies
12
Views
1K
Rigorous mathematical definition of sampling
    • Set Theory, Logic, Probability, Statistics
Replies
13
Views
2K
I Correct understanding of confidence intervals....
    • Set Theory, Logic, Probability, Statistics
Replies
22
Views
3K
I Calculating Probability with Poisson Distribution: Radioactive Source Counts
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
I What are the commonly used estimators in regression models?
    • Set Theory, Logic, Probability, Statistics
Replies
23
Views
2K
A Number of unequal integers with sum S
    • Set Theory, Logic, Probability, Statistics
Replies
12
Views
957

Hot Threads

Recent Insights

Back
Top