Probability
Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of "heads" equals the probability of "tails", so the probability is 1/2 (or 50%) chance of either "heads" or "tails".
Day 1 Theoretical and Experimental Probabilities
Experimental Probability
One way to find the probability of an event is to conduct an experiment.
Example:
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.
Solution:
Take a marble from the bag.
Record the color and return the marble.
Repeat a few times (maybe 10 times).
Count the number of times a blue marble was picked (Suppose it is 6).
The experimental probability of getting a blue marble from the bag is 6/10 = 3/5.
Experimental Probability
One way to find the probability of an event is to conduct an experiment.
Example:
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.
Solution:
Take a marble from the bag.
Record the color and return the marble.
Repeat a few times (maybe 10 times).
Count the number of times a blue marble was picked (Suppose it is 6).
The experimental probability of getting a blue marble from the bag is 6/10 = 3/5.
Theoretical Probability
We can also find the theoretical probability of an event.
The formula for theoretical probability of an event is:
P(event) = Number of favourable outcomes ÷ Number of total outcomes
Example 1:
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of getting a blue marble.
Solution:
There are 8 blue marbles. Therefore, the number of favorable outcomes = 8.
There are a total of 20 marbles. Therefore, the number of total outcomes = 20
P(event) = Number of favourable outcomes ÷ Number of total outcomes = 8/20 = 2/5
Example 2:
Find the probability of rolling an even number when you roll a die containing the numbers 1-6. Express the probability as a fraction, decimal, ratio and percent.
Solution:
The possible even numbers are 2, 4, 6. Number of favorable outcomes = 3.
Total number of outcomes = 6
P(event) = Number of favourable outcomes ÷ Number of total outcomes = 3/6 = 1/2
The probability = 1/2 (fraction) = 0.5 (decimal) = 1:2 (ratio) = 50% (percent)
We can also find the theoretical probability of an event.
The formula for theoretical probability of an event is:
P(event) = Number of favourable outcomes ÷ Number of total outcomes
Example 1:
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of getting a blue marble.
Solution:
There are 8 blue marbles. Therefore, the number of favorable outcomes = 8.
There are a total of 20 marbles. Therefore, the number of total outcomes = 20
P(event) = Number of favourable outcomes ÷ Number of total outcomes = 8/20 = 2/5
Example 2:
Find the probability of rolling an even number when you roll a die containing the numbers 1-6. Express the probability as a fraction, decimal, ratio and percent.
Solution:
The possible even numbers are 2, 4, 6. Number of favorable outcomes = 3.
Total number of outcomes = 6
P(event) = Number of favourable outcomes ÷ Number of total outcomes = 3/6 = 1/2
The probability = 1/2 (fraction) = 0.5 (decimal) = 1:2 (ratio) = 50% (percent)
Day 2 Calculating Probability