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

Explanation

Let's solve the problem step by step.

### Given:
A standard deck of 52 cards consists of:
- 13 Diamonds
- 13 Hearts
- 13 Clubs
- 13 Spades

### Total number of cards = 52

### (i) Probability that the card will be a diamond

**Step 1:** Identify the number of favorable outcomes.
- Number of diamond cards = 13

**Step 2:** Calculate the probability.
- Probability (P) of drawing a diamond = Number of diamond cards / Total number of cards
- \( P(\text{Diamond}) = \frac{13}{52} = \frac{1}{4} \)

### (ii) Probability that the card will not be an ace

**Step 1:** Identify the total number of aces.
- There are 4 aces in the deck (one for each suit).

**Step 2:** Calculate the probability of drawing an ace.
- Probability (P) of drawing an ace = Number of aces / Total number of cards
- \( P(\text{Ace}) = \frac{4}{52} = \frac{1}{13} \)

**Step 3:** Calculate the probability of not drawing an ace.
- \( P(\text{Not Ace}) = 1 - P(\text{Ace}) = 1 - \frac{1}{13} = \frac{12}{13} \)

### (iii) Probability that the card will be a black card (i.e., a club or a spade)

**Step 1:** Identify the number of black cards.
- Number of clubs = 13
- Number of spades = 13
- Total black cards = 13 + 13 = 26

**Step 2:** Calculate the probability.
- \( P(\text{Black Card}) = \frac{26}{52} = \frac{1}{2} \)

### (iv) Probability that the card will not be a diamond

**Step 1:** Calculate the probability of drawing a diamond (already calculated).
- \( P(\text{Diamond}) = \frac{1}{4} \)

**Step 2:** Calculate the probability of not drawing a diamond.
- \( P(\text{Not Diamond}) = 1 - P(\text{Diamond}) = 1 - \frac{1}{4} = \frac{3}{4} \)

### (v) Probability that the card will not be a black card

**Step 1:** Calculate the probability of drawing a black card (already calculated).
- \( P(\text{Black Card}) = \frac{1}{2} \)

**Step 2:** Calculate the probability of not drawing a black card.
- \( P(\text{Not Black Card}) = 1 - P(\text{Black Card}) = 1 - \frac{1}{2} = \frac{1}{2} \)

### Final Answers:
1. Probability of drawing a diamond = \( \frac{1}{4} \)
2. Probability of not drawing an ace = \( \frac{12}{13} \)
3. Probability of drawing a black card = \( \frac{1}{2} \)
4. Probability of not drawing a diamond = \( \frac{3}{4} \)
5. Probability of not drawing a black card = \( \frac{1}{2} \)