[Music]
probability
we probably use this word as often as
oh wait i already said it probably
most of you would probably know what the
probability of getting tails in a coin
flipping experiment is
but what is the definition of
probability
let's analyze what we already know about
it
probability is a measure of a likelihood
of an event occurring
the bigger the probability the more
likely it is that the event will occur
the lowest probability is zero and the
highest is one or one hundred percent
so it should be something that varies
between zero and one and grows when the
chance of success grows
to construct probability fairly we first
need to make a sample space which is a
set of all possible outcomes of an
experiment
for example
samples based for dice throwing
experiment is one two three four five
and six
sample space for coin flipping
experiment is heads or tails
for pulling one card out of a deck it's
for a result in a roulette round it's
sometimes it's not as obvious for
example try to write a sample space for
flipping two coins together
pause the video and try doing it
yourself first
the correct sample set is h
ht
th and
where h means heads and t is tails
we end up with four different events
because h t and t h are different
occurrences
so the probability of getting one heads
and one tails is higher than the
probability of getting two tails
after we construct a sample space it's
pretty easy to find the probability of
an event
we just need to find the ratio between
the number of outcomes that satisfy our
event and the total number of outcomes
for example let's find the probability
of getting more than nine as a sum of
two roll dice
our event is a sum that's greater than
nine
outcomes that satisfy our event are five
five
six four
four six
five six
six five
and six six
the number of all possible outcomes is 6
times 6 which equals 36
so our probability is 6 over 36 or 1 6.
another example what's the probability
of getting a card of spades or an ace
from a standard 52 card deck if we get
one out blindly
how many cards satisfy our event
we have 13 spades cards and four aces
so 13 plus 4 is 17
but we counted ace of spades two times
so there are only 16 cards as a result
our probability is 16 over 52 or 4 13.
and now a task for you there are three
blue five red and four yellow balls in a
hat
can you find what the probability of
getting a yellow ball from the hat with
only one try is
pause the video and try to find the
answer
the correct answer is a third or four
twelfths
there are four yellow balls the total
number of balls is twelve so our
probability
is four-twelfths or one-third
and finally what does probability show
and how can we use it
you could say that even if an event has
a probability of one in a million it
still may occur but it's so low why
would you even consider it
okay you're right but probability also
shows us that if you repeat an
experiment many times the ratio between
successful outcomes and all the outcomes
become closer to your probability of
success
if you repeat the experiment with
coloured balls nine thousand times you
will probably get a yellow ball in about
three thousand of them
that's why you definitely win on a
roulette table the longer you play
this is called the law of large numbers
watch the second part of this video to
find out what restrictions this approach
has and what its consequences are
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