QUESTION

# All the red faces cards are removed from a deck of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the card drawn is:i) A red cardii) A face cardiii) A card of clubs

Hint: Face cards are the king, queen and the jack cards. We will have to find the total outcomes and favourable outcomes in each case in order to determine the probability.

We know that there are 26 red cards in a deck of 52 cards and 6 red face cards are removed from the deck.
In a deck of playing cards there are 52 cards.
When all the red face cards are removed,
Total no. of cards left = 52 – 6 = 46
Total outcomes = 46.
$Probability = \dfrac{\text{No. of favourable outcomes}}{\text{Total no. of outcomes}}$

i) Let (R) be the event of getting a red card.
Total no. of red cards in the deck of 52 cards = 13 + 13 = 26
We removed 6 red face cards, so
Total red cards left = 26 – 6 = 20
No. of outcomes favorable in R = 20
$\Rightarrow P(R) = \dfrac{20}{46} = \dfrac {10}{23}$
$\therefore$ The probability of getting a red card = $\dfrac{10}{23}$

(ii) Let (F) be the event of getting a face card.
We know that there are a total of 12 face cards (6 red and 6 black). After removing 6 red face cards,
No. of face cards left = 12 – 6 = 6
No. of favorable outcomes in F = 6
$\Rightarrow P(F) = \dfrac{6}{46} = \dfrac {3}{23}$
$\therefore$ The probability of getting a face card = $\dfrac{3}{23}$

(iii) Let (C) be the event of getting a card of clubs.
The cards of clubs are black in colour, so nothing has been removed from it.
Total no. of club cards = 13
No. of favorable outcomes = 13
$\Rightarrow P(C) = \dfrac{13}{46}$
$\therefore$ The probability of getting a club card = $\dfrac{13}{23}$

Note: In these types of questions, firstly we have to write the sample space of the experiment based on the conditions provided, then find the favourable no. of outcomes and thereby finding the probability. All outcomes must be considered to avoid mistakes.