## 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

1. Kings of same color
2. Kings of different color
3. Not Kings at all
1. $$P(BUR) =P(B)+P(R)$$
• $$\frac{^2C_1 \times ^2C_1}{^{52}C_1\times ^{52}C_1}+\frac{^2C_1 \times ^2C_1}{^{52}C_1\times ^{52}C_1}$$ Why not $$^{52}C_2$$, $$^4C_2$$
1. $$1-P(B \cup R)$$
• $$P(K)= \frac{^4C_1 \times ^4C_1}{^{52}C_1\times ^{52}C_1}$$
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

1. an Ace