Probability is how likely is it that something will occur.
All probabilities are numbers between 0 and 1. A probability of 1 indicates 100% chance that something will occur. Probability of 0 implies 0% chance that something will occur.
A probability of getting a heads when we flip a coin once is 50% or 0.5
A probability value between 0 and 0.5 implies its most likely the event may not occur.
A probability value of 0.5 implies the event has an equal chance to occur or non-occur.
A probability value between 0.5 and 1 implies its most likely the event may occur.
Probability of an event occurring is expressed as
P(event) = (All possible outcomes that meet the criteria)/(All possible outcome)
Probability of a coin being flipped and we getting a tails is:
P(Tails) = 1/2 = 0.5
since in this case there are 2 possible outcomes (Heads and Tails)
Probability of flipping a dice and getting the number 5 is
P(5) = 1/6 = 0.16 (or 16%)
Since there can be 6 possible outcomes when we flip a coin (from 1...6)
What I described above is Theoretical Probability.
We also have Experimental Probability, which basically is probability when we conduct tests and record them.
e.g we flipped a dice 7 times and got the number five 4 times.
Whats the experimental probability?
P(5) = 4/7 = 0.57 (57%)
As per Law of Large numbers, the more experiments we conduct, we shall see that the Experimental probability value will get closer and closer to the Theoretical probability value.
The Addition Rule:
Definition:
The addition rule states the probability of two events is the sum of the probability that either will happen minus the probability that both will happen.
e.g.
What is the probability of getting a "Heads" if we flip a coin 2 times?
When we flip a coin, the options we have is:
Heads - Heads
Heads - Tails
Tails - Heads
Tails - Tails
So by the definition of the addition rule:
P(Heads) = P(Getting heads in the first flip) + P(Getting heads in the second flip) - P(Both flips we get heads)
P(Heads) = (2/4) + (2/4) - (1/4) = 3/4 = 75%
