Question

From a well shuffled pack of 52 cards, two black kings and two black jacks are removed. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is neither an ace nor a king.

Answer 1

Given: A well-shuffled 52-card pack; two black kings and two black jacks are removed. One card is then drawn from the remaining pack. Find P(card is neither an ace nor a king).

Step-wise calculation:

1. Total cards remaining

= 52 – 4

= 48

2. Number of aces remaining = 4 (None were removed).

3. Number of kings remaining

= 4 – 2 (Two black kings removed, leaving the two red kings)

= 2 

4. Number of cards that are ace or king

= 4 + 2

= 6

5. Number of favourable cards (Neither ace nor king)

= 48 – 6

= 42

6. Required probability

= `42/48`

= `7/8`

The probability that the drawn card is neither an ace nor a king = `7/8`.