One card is drawn from a well shuffled deck o 52 cards. If each outcome is equally likely, calculate the probabilty that the card will be:
(i)a diamond
(ii) not a diamond
(iii) not an ace
(iv) a black card (i.e.a club or a spade)
v. not a black card.

Answer

To solve the problem step by step, we will calculate the probabilities for each of the specified cases when one card is drawn from a well-shuffled deck of 52 cards.

### Step-by-Step Solution:

1. **Probability of drawing a diamond:**
- In a standard deck of cards, there are 13 diamonds.
- The total number of cards is 52.
- The probability \( P(\text{Diamond}) \) is given by:
\[ P(\text{Diamond}) = \frac{\text{Number of Diamonds}}{\text{Total Number of Cards}} = \frac{13}{52} = \frac{1}{4} \]

2. **Probability of not drawing a diamond:**
- The probability of not drawing a diamond can be calculated using the complement rule:
\[ P(\text{Not Diamond}) = 1 - P(\text{Diamond}) = 1 - \frac{1}{4} = \frac{3}{4} \]
- Alternatively, since there are 39 cards that are not diamonds (52 total cards - 13 diamonds):
\[ P(\text{Not Diamond}) = \frac{39}{52} = \frac{3}{4} \]

3. **Probability of not drawing an ace:**
- There are 4 aces in a standard deck of cards.
- The probability of drawing an ace is:
\[ P(\text{Ace}) = \frac{4}{52} \]
- Thus, the probability of not drawing an ace is:
\[ P(\text{Not Ace}) = 1 - P(\text{Ace}) = 1 - \frac{4}{52} = \frac{48}{52} = \frac{12}{13} \]

4. **Probability of drawing a black card (club or spade):**
- There are 26 black cards in total (13 clubs + 13 spades).
- The probability of drawing a black card is:
\[ P(\text{Black Card}) = \frac{26}{52} = \frac{1}{2} \]

5. **Probability of not drawing a black card:**
- The probability of not drawing a black card can also be calculated using the complement rule:
\[ P(\text{Not Black Card}) = 1 - P(\text{Black Card}) = 1 - \frac{1}{2} = \frac{1}{2} \]
- Alternatively, since there are 26 red cards (hearts + diamonds):
\[ P(\text{Not Black Card}) = \frac{26}{52} = \frac{1}{2} \]

### Summary of Probabilities:
- (i) Probability of drawing a diamond: \( \frac{1}{4} \)
- (ii) Probability of not drawing a diamond: \( \frac{3}{4} \)
- (iii) Probability of not drawing an ace: \( \frac{12}{13} \)
- (iv) Probability of drawing a black card: \( \frac{1}{2} \)
- (v) Probability of not drawing a black card: \( \frac{1}{2} \)