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Module 1-3
Probability

Probability: is a number between 0 and 1 (fraction) that tells how likely it is that an event will take place.

The closer to 1 the more likely it is that the event will occur.
A probability of one, means that the event will always occur.
A probability of zero, means that the event will never occur.
Outcomes are equally likely if they have the same chance of occurring.

Event: What outcome you are testing.
Outcome: What actually happens.

Example, in a bag of colored marbles, the event would be the likelihood of picking a particular color.
If there were 3 red, 4 blue and 3 green marbles, what is the likelihood of picking a red marble?

Experimental probability: When you actually do the event (toss a coin) and count up the actual outcomes. Example: I toss a coin 50 times and 29 out of 50 land on heads.

Theoretical probability: You donít actually do the experiment. Count up how many possible positive outcomes there can be over how many actual outcomes there are.

Example 1: On a fair coin there is one head, and one tail. That means there is a total of 2 possible outcomes. The probability of getting a head is 1 out of 2 or .
Compare the result of the experimental probability to the theoretical probability. Notice, they are not the same!

Example 2: If there were 3 red, 4 blue and 3 green marbles, what is the likelihood of picking a red marble?
The number of positive possible outcomes is 3, because there are 3 red marbles; the number of total outcomes is 10, so the theoretical probability of picking a red marble is
.

Example 3: If there were 3 red, 4 blue and 3 green marbles, what is the P(red or blue)? Notice how we wrote this probability question. It means what is the probability of picking a red or a blue marble. Since there are 3 red marbles and 4 blue marbles there are 7 possible positive outcomes out of 10 total possible outcomes so the P(red or blue) is .

Example 4: If there were 3 red, 4 blue and 3 green marbles, what is the P(red and blue)? Notice the and between red and blue. If we are only picking one marble, it is impossible to pick a red and a blue marble, therefore the P(red and blue is 0.