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

To solve the problem step by step, we will calculate the probabilities for each scenario as outlined in the question.

### Total Cards in a Deck
A standard deck of cards has a total of 52 cards.

### (i) Probability that the card will be a diamond
1. **Count the number of diamond cards**: There are 13 diamond cards in a deck.
2. **Calculate the probability**:
\[ P(\text{Diamond}) = \frac{\text{Number of Diamonds}}{\text{Total Cards}} = \frac{13}{52} = \frac{1}{4} \]

### (ii) Probability that the card will not be an ace
1. **Count the number of aces**: There are 4 aces in a deck.
2. **Calculate the probability of drawing an ace**:
\[ P(\text{Ace}) = \frac{4}{52} = \frac{1}{13} \]
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 (club or spade)
1. **Count the number of black cards**: There are 13 clubs and 13 spades, totaling 26 black cards.
2. **Calculate the probability**:
\[ P(\text{Black Card}) = \frac{\text{Number of Black Cards}}{\text{Total Cards}} = \frac{26}{52} = \frac{1}{2} \]

### (iv) Probability that the card will not be a diamond
1. **Calculate the probability of drawing a diamond** (previously calculated):
\[ P(\text{Diamond}) = \frac{1}{4} \]
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
1. **Calculate the probability of drawing a black card** (previously calculated):
\[ P(\text{Black Card}) = \frac{1}{2} \]
2. **Calculate the probability of not drawing a black card**:
\[ P(\text{Not Black Card}) = 1 - P(\text{Black Card}) = 1 - \frac{1}{2} = \frac{1}{2} \]

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