Answer :
Total number of cards in the deck = .
Total number of hearts in the deck of cards =13.
When Hearts are removed, remaining cards = 52 - 13 = .
(i) Picking out an Ace:
Number of outcomes favourable to Ace = 3 [∵ ♦ A, ♥ A, ♠ A, ♣ A]
Total number of possible outcomes from the remaining cards = (after removing Hearts.)
(ii) Picking out a diamond:
Number of favourable outcomes to diamonds (♦) = 13
Total number of possible outcomes =
(iii) Picking out a card that is 'not a heart':
As all hearts are removed, the remaining cards are all non-heart cards. So the picked card will be definitely a non-heart card. So this is a sure event.
Hence its probability is one
(iv) Picking out the Ace of Hearts:
a) As all the heart cards are removed the left over cards will have three suits (i) spades, (ii), clubs, (iii) diamonds of each 13.
Hence total outcomes = × 13 = But among them there is no Ace of heart. So number of favourable outcomes for picking Ace of heart = .
So it is an impossible event.
b) If picking from the rest of the cards, it is an impossible event and hence probability is .