From a deck, remove K, Q, J of clubs; draw one card from remaining. Probability that card is (i) a heart (ii) a king?
(i) \(\dfrac{13}{49}\), (ii) \(\dfrac{3}{49}\)
Step 1: A standard deck has 52 cards.
Step 2: We are removing 3 cards: King of clubs, Queen of clubs, Jack of clubs.
Step 3: So, number of cards left = 52 − 3 = 49.
(i) Probability of drawing a heart:
There are 13 hearts in a full deck. Removing K, Q, J of clubs does not affect the hearts.
So, number of favourable outcomes = 13.
Total outcomes = 49.
Therefore, probability = \(\dfrac{13}{49}\).
(ii) Probability of drawing a king:
In a full deck, there are 4 kings (one from each suit: hearts, diamonds, clubs, spades).
We removed the King of clubs, so only 3 kings remain.
So, number of favourable outcomes = 3.
Total outcomes = 49.
Therefore, probability = \(\dfrac{3}{49}\).