The probability that a card drawn from a pack of 52 cards will be a diamond or king is

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  1. \(\frac{1}{52}\)
  2. \(\frac{2}{13}\)
  3. \(\frac{4}{13}\)
  4. \(\frac{1}{13}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{4}{13}\)
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Detailed Solution

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Concept Used:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Calculation:

Total number of cards = 52

Number of diamond cards = 13

Number of king cards = 4

Number of cards that are both diamond and king = 1

Number of favorable outcomes (diamond or king) = (Number of diamond cards) + (Number of king cards) - (Number of cards that are both diamond and king)

⇒ Number of favorable outcomes = 13 + 4 - 1 = 16

Probability of drawing a diamond or a king = (Number of favorable outcomes) / (Total number of cards)

⇒ Probability = 16 / 52

⇒ Probability = 4 / 13

∴ The probability that a card drawn from a pack of 52 cards will be a diamond or king is 4/13.

Hence option 3 is correct

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