Question

The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards, finding the probability of getting a face card?

Answer 1

From the pack of 52 cards three cards are removed and hence we get the new sample space to be 49 and now the face cards in the remaining set is 3 in clover, 3 in heart and 3 in diamond so the number of face cards is 9 hence the probability of drawing a face card from the remaining cards is given by $P\left( A \right) = \dfrac{{n\left( A \right)}}{{n\left( {{S^{'}}} \right)}}$.

Step by step solution :
We know that a pack of cards contain 52 cards
Hence the total number of cards is 52
That is $n\left( S \right) = 52$ , where S is the sample space
We need to remove the king , queen and jack of clubs from these 52 cards
Hence now we get the total number of cards to be $52 - 3 = 49$
Now $n\left( {{S^{'}}} \right) = 49$ , where ${S^{'}}$is the new sample space
Now we are asked for the probability of drawing a face card from the remaining cards
Now we have three face cards in clover , three face cards in hearts and three face cards in diamond
Hence there are 9 face cards in the remaining set of cards
If A is the event of drawing a face card
Then $n\left( A \right) = 9$
Hence the probability of drawing a face card is given by
$\Rightarrow P\left( A \right) = \dfrac{{n\left( A \right)}}{{n\left( {{S^{'}}} \right)}}$
Using the known values we get
$\Rightarrow P\left( A \right) = \dfrac{9}{{49}}$

Hence the probability of getting a face card from the remaining cards is $\dfrac{9}{{49}}$.

Note :
A probability of 0 means that an event is impossible. A probability of 1 means that an event is certain. An event with a higher probability is more likely to occur. Probabilities are always between 0 and 1. The probabilities of our different outcomes must sum to 1.