Probability and statistics

In summary: So the probability is \frac{\binom{3}{1}\binom{17}{3}}{\binom{20}{4}}.In summary, the conversation revolves around a person seeking help with probability problems and struggling to understand the logic behind certain solutions. The conversation includes examples of car rental probabilities and tire defects, with the final question being about solving for a probability given other known probabilities.
  • #1
philipc
57
0
I'm not having much luck learning from the examples in my probability book, they only do the most of basic examples, I'm in need of some good examples and solutions, any ideas?

For example here is the problem I'm trying to work on
A car rental agency has 18 compact cars and 12 mid-size cars, if 4 are randomly selected, what is the probability of getting two of each kind?

I'm not sure how to set up the equations
Thanks
Philip
 
Physics news on Phys.org
  • #2
What have you tried, my friend? Just use the multiplication rule. :bugeye:
 
  • #3
sorry your reply didn't help
 
  • #4
What Have You Tried?
 
  • #5
Nvm, here we go. Let us assume that randomly selected means that each of the [itex]\binom{30}{4}[/itex] combinations is equally likely to be selected. Hence the desired proability equals
[tex]\frac{\binom{18}{2}\binom{12}{2}}{\binom{30}{4}}[/tex]
 
  • #6
That gives the correct results thank,
my problem I'm still having a hard time following the logic behind picking the numbers to work with.

Here is another example from the book I can't find the logic
If 3 of 20 tires are defective and 4 of them are picked randomly, what is the probability that only one of the defective one will be included.
So I tried this
[tex]\frac{\binom{17}{3}}{\binom{30}{4}}[/tex]
this would give your total probability of receiving any number of bad tires right?
But the book wants just one bad tire so they use
[tex]\frac{\binom{3}{1}\binom{17}{3}}{\binom{20}{4}}[/tex]
this is the logic I can't follow, can you explain why they choose these numbers?
Thanks
Philip
 
  • #7
Got one more let's say P(A|B) = .2 and I know P(B) to be .65, how can I solve for P(A)?
 
Last edited:
  • #8
There are totally 20 tires (17 proper and 3 defective).

Experiment 1: Pick one defective tire. One (exactly one) defective tire can be picked in [itex]\binom{3}{1}[/itex] different ways.

Experiment 2: Pick three proper tires. This can be done in [itex]\binom{17}{3}[/itex]
Using the basic principle of counting we got [itex]\binom{3}{1}\binom{17}{3}[/itex] different ways to pick 1 defective and 3 proper tires among 20.
 

What is the difference between probability and statistics?

Probability is the branch of mathematics that deals with the likelihood of events occurring, while statistics is the branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data.

What are the basic concepts of probability?

The basic concepts of probability include outcomes, events, sample space, probability, and independence. Outcomes are all possible results of an experiment, events are combinations of outcomes, sample space is the set of all possible outcomes, probability is the likelihood of an event occurring, and independence is when the occurrence of one event does not affect the occurrence of another event.

What are the different types of probability?

The different types of probability include classical, empirical, subjective, and conditional. Classical probability is based on equally likely outcomes, empirical probability is based on observations and data, subjective probability is based on personal beliefs and opinions, and conditional probability is the probability of an event occurring given that another event has already occurred.

What is the purpose of statistics?

The purpose of statistics is to collect data, analyze it, and make inferences or conclusions about a population based on the data. It helps to make informed decisions and predictions, and also allows for the testing of hypotheses and theories.

What are the measures of central tendency?

The measures of central tendency are mean, median, and mode. Mean is the average of a set of data, median is the middle value when the data is arranged in ascending or descending order, and mode is the most frequently occurring value in the data set.

Similar threads

  • STEM Academic Advising
Replies
27
Views
1K
  • Programming and Computer Science
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
160
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
11
Views
970
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
Replies
15
Views
899
  • Introductory Physics Homework Help
Replies
2
Views
875
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
Back
Top