A card is drawn randomly
from a standard 52-card deck pictured here below.
We're asked to determine the following probabilities.
Remember, the probability of an event, E,
is equal to the favorable number of outcomes
divided by the total number of outcomes.
In this case, because we're drawing one card
from a 52-card deck,
the total number of outcomes will always be 52.
We are first asked to find the probability
the card is a three.
So looking at the cards below.
We have the aces, the twos, and here are the threes.
Notice there are four threes in the deck,
which means there are four favorable outcomes
out of a total of 52 outcomes,
and therefore the probability the card is a three
is four divided by 52 or 4/52, which does simplify.
The greatest common factor between four and 52 is four,
so we divide both by four to simplify.
The simplified probability is 1/13.
Probability can also be expressed
as a decimal and a percentage.
Let's also show those two forms.
To convert 1/13 to a decimal, we divide one by 13.
And let's round to four decimal places,
which is 0.769
or 0.0769,
which is equal to 7.69%.
Remember, the exact probability is 1/13.
These two are rounded.
Next, we're asked to find the probability
the card is a black eight.
So going back to the deck of cards,
again, we have the aces, the two, threes,
fours, fives, six, sevens, and eights.
Notice how there are two black eights.
There is an eight of spades, and there is an eight of clubs.
So there are a total of two favorable outcomes
out of a total of 52 outcomes.
The probability is two divided by 52 or 2/52.
Simplifying, we divide the numerator
and denominator by two, which gives us 1/26.
And again, let's also show the decimal in percentage.
So one divided by 26
to four decimal places is 0.0385,
which is 3.85%.
Next, we're asked to find the probability
the card is a face card.
Face cards are jacks, queens, and kings,
which are these 12 cards here,
which means there are 12 favorable outcomes
out of a total of 52 outcomes,
and therefore the probability is 12/52
or 12 divided by 52.
Simplifying, we divide both by four,
which gives us 3/13.
And again, let's show the decimal in percentage.
Three divided by 13
to four decimal places is 0.2308,
which gives us 23.08%.
And for the last example,
we're asked to find the probability the card is not a heart.
So the hearts are in this row here,
and therefore all the other cards
would be favorable outcomes.
So we have 13 favorable outcomes here with the spades
and then 13 favorable outcomes here with diamonds
and 13 more with the clubs,
which gives us a total of 26 favorable outcomes here.
Again, we have 13 favorable outcomes here,
26 favorable outcomes here,
which gives a total of 39 favorable outcomes
or 39 cards that are not a heart,
and therefore the probability of not a heart
is 39 divided by 52 or 39/52.
The greatest common factor between 39 and 52 is 13.
So we divide both by 13.
39 divided by 13 is three,
52 divided by 13 is four,
which gives us a probability of 3/4,
which as a decimal is 0.75 which as a percentage is 75%.
I hope you found this helpful.