Rolling a die, drawing a card out of a deck, and flipping a coin are all things we're familiar
with and these are often used to discuss the basic concepts of probability. There are 4
key terms that are often used with probability, a probability experiment, which is a process where
specific results are obtained, such as rolling a die as there are only six possible outcomes.
And outcome is another key term, which is a single result of a probability experiment, so, if you draw
a four of hearts from a full deck of cards that is an outcome. Sample space is another key term
and it is a set of all possible outcomes for a probability experiment. For instance the sample
space for rolling two dice is here, and you can see the possible outcomes for die one and the possible
outcomes for die number two, and the sample space is the pairs of numbers listed on the chart
here. So there are 36 possible outcomes in this sample space. Event is another key term used in
probability and an event is a set of outcomes of a probability experiment, it is a subset of
the sample space, and an event with one outcome is a simple event, and a compound event consists
of two or more outcomes. For instance the event of rolling a four on a die roll is a simple event, and
the event of getting an even number on a die roll is a compound event. There are three main types
of probability, classical probability, empirical probability, and subjective probability. Classical
probability is used when each outcome in a sample space is equally likely to occur. For instance the
sample space for rolling two dice, and each of these outcomes has the same chance to occur. The formula
for this is P of E, probability of any event, equals the number of outcomes in event E, divided by the
total number of outcomes in the sample space. So the probability of the two dice totaling 5
is P of 5 equals, 4 the number of possible combinations the total up to 5, divided by 36,
the total number of outcomes in the sample space. Empirical probability is when each outcome is not
equally likely to occur and it is based on observations obtained from experiments. For
instance let's say you polled 50 people and ask them what their favorite sport is. Using a frequency
table, 29 said football, 11 said basketball, 6 said baseball, 3 said soccer and 1 said tennis.
Now we can compute probabilities for each of the categories. The formula for empirical probability
is the probability of event, equals frequency for the class or the event, divided by the total of the
frequencies. So the probability of football being a person's favorite sport is 29 divided by 50,
which is 0.58, and the probability of tennis being someone's favorite sport is 1 divided by 50, which
is 0.02, and you can convert these to percentages by multiplying by 100 to get 58%, and
2%. Subjective probability is based on an educated guess or an estimate. For instance if I
were to say there was a 73% chance the Yankees win the World Series next year, this is based on
my experience and evaluation. And there are 4 key rules to probability. The first is that probability
of an event is between 0 and 1, including 0 and 1, and this is written as 0 less than or equal to the
probability of an event, less than or equal to 1. And whatever the value of P is, can be written as
a fraction or decimal. For instance the probability of getting a head on a coin toss is 0.5, or 1 over 2.
Rule number two is that the sum of all possible outcomes in a sample space is 1. So the sample
space for a die roll is 1 through 6, with each having a 1 over 6 probability of occurring, add
these up, and we get 1. Rule number three is if it is impossible for a given event to occur, so it's
not part of the sample space, its probability is zero. For instance the probability of rolling 8
on a die roll is not part of the sample space, so its probability is zero. Rule number four is that
if an event is certain to occur, its probability is 1. So the probability of rolling a 1 through
a 6 on a die roll is certain to happen, so its probability is 1. Alright my friends, hopefully
this video helped you out, I do have more videos right there for you, till next time, I am outta here.