Jenelle draws one card
from a standard deck of 52 cards.
Determine the probability of drawing
either a queen or a king.
Then determine the probability
of drawing either a ten or a club.
In this video, we will determine the probabilities
by using the idea that we know that probability is equal to
the favorable number of outcomes
divided by the total number of outcomes.
In the next video, we'll show how to find
the same probabilities using one of the appropriate formulas
shown here below for mutually exclusive events
and events that are not mutually exclusive.
Again, in this video, we will just use
the idea of basic probability.
So we know Jenelle was drawing
one card from a deck of cards.
And therefore, there are 52 possible outcomes.
And we're first asked to determine the probability
of drawing either a queen or a king.
Let's indicate this as the probability
of Q for queen or K for king.
So, because it reads a queen or a king,
a queen or a king is a favorable outcome.
And because there are four queens and four kings,
we have a total of eight favorable outcomes
out of a total of 52 outcomes.
And therefore, the probability of drawing
a queen or a king is eight out of 52, or 8/52.
As a fraction that simplifies,
the greatest common factor between eight and 52 is four,
so we divide both by four to simplify.
The simplified probability is 2/13.
So the probability of selecting a queen or a king
is equal to 2/13.
Let's also express this as a decimal and percent.
2/13 to four decimal places is approximately 0.1538
which is equal to 15.38%.
The events of selecting a queen and selecting a king
are called mutually exclusive,
because the two events cannot occur at the same time,
meaning we cannot select a card
that is a queen and a king at the same time.
So if we were going to use a formula,
we would use this formula here,
which we'll explain in more detail in the next video.
Next, we're asked to find the probability
of drawing either a 10 or a club.
Let's indicate this as the probability of a 10 or club.
So if a card is a 10 or a club, it is a favorable outcome.
Well, we know there are four 10's in a deck and 13 clubs.
But because a card can be both a club and a 10,
we need to be very careful when counting
the favorable outcomes.
So looking at the possible outcomes, here we have the clubs,
and in this column, we have the 10's.
So these are all the favorable outcomes.
We have 13 along the bottom, and then 14, 15, 16.
There are 16 favorable outcomes
out of a total of 52 outcomes.
And therefore, the probability of selecting
a 10 or a club is 16 divided by 52, or 16/52.
So notice how we didn't just add the number of clubs
and the number of 10's.
That would've given us, 13 plus four,
17 favorable outcomes, but if we did that,
we would've counted the 10 of clubs twice.
And therefore, we have to be careful
when the events are not mutually exclusive,
meaning when the two events can occur at the same time
or it's possible to have a card
that is both a 10 and a club.
So we can still use the basic idea of probability
to answer these questions.
We just need to be careful about determining
the total number of favorable outcomes.
Now let's go ahead and simplify this probability
by dividing both by four.
The simplified probability is 4/13.
Let's go ahead and find the decimal and the percent.
4/13 to four decimal places is approximately 0.3077,
which is 30.77%.
So, again, in the next video,
we'll talk more about how we can use
the appropriate formula shown below
to determine these same probabilities.
I hope you found this helpful.