Probability plays a large role in our society. There are many types of probability. The videos in this section will address some of the types of probability as well as calculating the odds for or against an event occurring. We will also explore expected values and counting methods.
In this section, we will look at different types of probability. We will also look at several examples of finding probability.
Theoretical or Classical
Theoretic Probability of Playing Cards
Experimental or Empirical
Probability Rules
In this section, we will look at different rules utilized in Probability. The videos will include topics like Bayes Rule, And and Or probabilities, and probabilities using two-way tables or contingency tables. There are two rules for both "and" and "or" probabilities. The videos below demonstrate both of the rules for both types.
Probability from a Two-Way Table
Experimental Probability from Frequency Table
Bayes Rule to Find Probability of Disease given the Test was Positive
"Or" Probability Rules with Example Using Playing Cards
In this section, we will explore calculating the odds for or against an event happening. The odds for winning puts the probability of success on top, where the odds against puts the probability of failure on top. You can also calculate the probability of success or failure given the odds of an event happening.
Odds For
Odds Against
Find Probability Given Odds Against
Find Probability Given Odds For
Expected Value
Being able to calculate the expected value is an important part of business analysis. The videos show how to calculate the expected value. If the expected value is positive, then it is a gain. If the expected value is negative, then it is a loss. If the expected value is zero, that means you break even. Also, the videos address how to calculate a fair price, which means the expected value is zero.
Expected Value and Fair Price
Expected Value of Making a Purchase
Tree Diagrams
Tree diagrams can be a useful tool to visualize the sample space of a particular probability experiment. They can also be used to help find the probability of certain events happening, because of the ease of finding the sample space. The disadvantage of tree diagrams is that they take up a lot of space, and are not practical for a large sample space.
Counting is an important part of probability. It is important to be able to find the total number of possibilities an event occur. Counting rules include the fundamental counting principal, combinations and permutations. We need to be able to find the total possible number of outcomes to find the probability. Finding probability using these principals will also be demonstrated.
Fundamental Counting Principal
Finding Number of Passwords
Permutations Defined
Combinations Defined
Permutations Arranging All Items
Permutations Selecting Some
Combinations
Combinations TI-84
Combinations TI-Nspire
Multiple Combinations
Multiple Combinations TI-84
Multiple Combinations TI-Nspire
Probability with Combinations and Permutations
After knowing how to use the counting techniques, you can then find probabilities. The videos in this section show how to find probabilities that involve permutations and combinations.
Probability of Matching 5 of 6 Numbers in a 43 Number Lottery