A card is drawn from a pack of 52 cards - Leaving Cert Mathematics - Question b - 2012

To find the probability of drawing either a club or a picture card, we first identify the number of clubs and picture cards:

• Number of clubs = 13
• Picture cards (Kings, Queens, Jacks) = 3 in each suit, total for all suits = 3 × 4 = 12

However, since the king of clubs has already been counted as a club, it is included in both categories.

Thus, the total number of unique clubs or picture cards:

Number of unique clubs or picture cards = Number of clubs + Number of picture cards - Picture cards that are clubs = 13 + 12 - 1 = 24

Now we find the probability:

$P( ext{club or picture card}) = \frac{24}{52} = \frac{6}{13}$

To find the probability that two cards drawn are neither clubs nor picture cards, we first determine the number of such cards in a standard deck:

• Total cards = 52
• Clubs = 13
• Picture cards = 12

Thus, the number of cards that are neither:

$52 - (13 + 12) = 27$

Now, we want the probability that both cards drawn are from these 27 cards:

For the first card: $P( ext{first card not a club or picture}) = \frac{27}{52}$

For the second card (after one card has been drawn, we have 26 left that are neither clubs nor picture cards): $P( ext{second card not a club or picture}) = \frac{26}{51}$

Therefore, the combined probability is:

$P( ext{both not clubs or picture}) = \frac{27}{52} \times \frac{26}{51} = \frac{702}{2652} \approx 0.26$

Thus, rounding to two decimal places: $P( ext{not club or picture card}) ext{ is } 0.26$