8.8 Playing Card
8.8.1 Concepts (Playing Card)
Each rank has 13 cards.
- Ace (A)
- King (K)
- Queen (Q)
- Jack (J)
- Numbers: 2, 3, 4, 5, 6, 7, 8, 9, 10
- 4+9 numbers = 13 cards.
8.8.2 Card Problem #01
3 cards are drawn from a pack of 52 cards. What is the probability that they are all Kings?
There are 4 Kings. We’ve to draw 3 cards.
- \(P(K) =\frac{^4C_3}{{^52}C_3}\)
8.8.3 Card Problem #02
If a card is drawn from a deck of 52 cards with 4 aces, what is the probability that an ace will not show up?
Let, P(A) = Ace appears
- \(1-P(A)\)
- \(1-\frac 1 {13}\)
8.8.4 Card Problem #03
Two cards are drawn with replacement; What is the probability that they are
- Kings of same color
- Kings of different color
- Not Kings at all
- \(P(BUR) =P(B)+P(R)\)
- \(\frac{^2C_1 \times ^2C_1}{^{52}C_1\times ^{52}C_1}+\frac{^2C_1 \times ^2C_1}{^{52}C_1\times ^{52}C_1}\) Why not \(^{52}C_2\), \(^4C_2\)
- \(1-P(B \cup R)\)
- \(P(K)= \frac{^4C_1 \times ^4C_1}{^{52}C_1\times ^{52}C_1}\)
- \(1-P(K)\)
8.8.5 Card Problem #04
A card is drawn from a pack of 52 cards. What is the probability that it is
- an Ace
- A Spade
- A Hearts or a King