Rahim removes all the hearts from the cards. What is the probability of

i. Picking out an ace from the remaining pack.

ii. Picking out a diamond.

iii. Picking out a card that is not a heart.

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Total number of cards in the deck = 52.

Total number of hearts in the deck of cards =13.

When Hearts are removed, remaining cards = 52 – 13 = 39.

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 = 39

– after removing Hearts.

Probability = P(A)

\(=\frac{No.\,of\,favourable \,outcomes}{Total\, no.\,of \,outcomes}\)

\(=\frac{3}{39}= \frac{1}{13}\)

ii) Picking out a diamond:Number of favourable outcomes to diamonds (♦) = 13

Total number of possible outcomes = 39

∴ p(♦) \(=\frac{3}{39}= \frac{1}{13}\)

iii) Picking out a card that is ‘not a heart’:As all hearts are removed, the remain-ing 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

P(E) \(=\frac{39}{39}= 1\)