### Video Transcript

A card is drawn at random from a
well-shuffled pack of 52 playing cards. Find the probability of getting
neither a red card nor a queen.

We’re told that the pack of cards
is well shuffled, and that we draw a card at random from it. That means that each card is
equally likely to be drawn. When we are dealing with equally
likely outcomes, the probability of an event is a fraction, where the denominator is
the total number of equally likely outcomes and the numerator is the number of those
equally likely outcomes that are favorable. That is, that are part of the
event.

The event that we’re interested in
is that of drawing neither a red card nor a queen. The number of equally likely
outcomes is the total number of cards, each of which is equally likely to be
drawn. And the number of favorable
outcomes is the number of favorable cards. That is, cards which are neither
red nor a queen. Well, if we didn’t know already,
then we’re told in the question that a standard deck of playing cards has 52
cards. And so the total number of cards is
52.

The question is how many of those
cards are neither red nor a queen. There are 13 cards in each suit,
the ace, two, three, four, five, six, seven, eight, nine, 10, jack, queen, and
king. And there are four suits, the
hearts and diamonds, which are both red, and the clubs and spades, which are
black. That gives 52 cards in total. You can count them all if you’d
like. We’re looking for those which are
neither a red card nor a queen. So we get rid of all the
hearts. They are all red, as are the
diamonds.

Now, we’ve got rid of the red
cards. Let’s get rid of the queens. Two of the queens are red and have
already been crossed out, the queen of hearts and the queen of diamonds. We only have to cross out the queen
of clubs and the queen of spades.

The cards we are left with are
neither red nor a queen. How many of them are there? Well, we can count them up. And if we do so, we find that there
are 24. So let’s substitute 24 for the
number of cards which aren’t red or a queen. We find that the probability of
drawing neither a red card nor a queen is then 24 over 52. We can simplify this fraction by
dividing both numerator and denominator by four, to find that the probability of
getting neither a red card nor a queen when drawing a card at random from a
well-shuffled pack of 52 playing cards is six over 13.