Week 12: The Probability of an Event

Probability is somethign that has been looked at multiple times throughout ones childhood. There’s the probability of getting 5 cards out of 52. There’s the probability of finding 1/2 of a goldfish than a whole goldfish. There is multiple types of probability.

Though these are some words needed to know probability

Outcome means experiments result

sample space means a set of all outcomes (s)

event means the subset of sample space (E) or what you want to happen.

then there is a probability of an event, which is

P(E)=n(E)/n(s) or # of ways E can occur/ # of ways of all outcomes

The easy way of probability is trying to find the probability of dices on certain amounts like

ex: on a single roll of a fair dice, find the probability of:

a) rolling of a 4: 1/6

b) rolling an odd #: 1/2

c) a # that is not a 4: 5/6

But there are harder ones too using nPr or nCr. 

For example. 

A bag contains 5 white marbles & 3 red marbles. A person draws 3 marblse. What is the probability all marbles are white?

n(white)/ n(draw 3)

C(5, 3)=10

C(8, 3)=56

so its equal to 10/56 or 5/28

Then there is a complement of an event which is a set of outcomes that do not belong to an event (E^1)

P(E^1)=1-P(E)

One example is:

If 5 cards are drawn from a deck of 52, without replacement. Find the probability of at least one ace?

P(no aces)=

C(48, 5)= 1712304

C(52, 5)= 2598960

1- 1712304/259860

=0.341158

Then there is mutually exclusive which is 2 events with no outcomes in common so what you do is look for what they do have in common. 

This is what you use to solve them:

P(E1 U E2)=P(E1)+P(E2)-P(E1upside down Union E2)

the U is union and the upside down union is called interaction

Above are examples on how you solve. 

That is how you do probability.

SEE YOU NEXT WEEK!!!