# Video: CBSE Class X • Pack 3 • 2016 • Question 4

CBSE Class X • Pack 3 • 2016 • Question 4

02:50

### 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.