Finding Probability
Theoretical probability is represented by the ratio of desired outcomes to the total possible outcomes
The probability of an event is a number from 0 to 1, including 0 and 1. The closer a
probability is to 1, the more likely it is to happen.
Steps for finding probability
Probabilities are represented in various forms including rational numbers, decimals, and percents. So another way to represent the answer for this problem would be 0.30 or 30%.
A special relationship exists between the desired probability of an event and its complement, their sum is equal to 1.
If the probability of drawing a 2 out of the hat is 3/10, then the complement is 1-Probability(drawing a 2).
1-(3/10)=7/10 or 0.70 or 70%.
C=1-P(event)
Use a tree diagram or and organizedlist to find the sample space.
Tree Diagram: A tree diagram is one way to organize and figure out all possibilities for events occurring
The first step is to take one of the events and write all of the possibilities. Start with flipping a coin, what are all of the possibilities for flipping a coin? They are heads and tails, so I write heads and tails.
Next, I am going to take a second event, in this case a second coin. I am going to think through all of the possibilities for flipping a coin. They are heads and tails.
From each of the possibilities in the first event, I will write all of the possibilities for the second event.
Lastly, I want to finish off each branch by writing the total possibility for each event. So, I will write heads, heads; heads tails; tails, heads; tails, tails.
I can count each branch to know the total number of possible outcomes and the total number of desired outcomes.
Organized list: Another way to figure out the total number of possible outcomes is to list them out in a systematic way
Just like with tree diagrams, it is important to start with one category and to list all of the possibilities with that category before moving on to the next category.
The total number of rows gives you the total number of possible outcomes. Add the number of favorable outcomes to find the probability.
What is the probability of getting heads, heads? 1/4
Sample Space
The sample space of an experiment is the set of all possible outcomes of that experiment.
Outcomes: A possible result of a probability experiment is called an outcome