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Let's go through each part of the problem step by step.

### Information about the Deck
- A standard deck has 52 cards.
- Cards are ranked from 2 through 10, Jack, Queen, King, and Ace.
- There are 4 suits (hearts, diamonds, clubs, and spades), with each suit having 13 cards.

### Part (a): Probability of a card **under a 4**
Cards under a 4 are: 2, and 3 (Ace is considered high here). Each of these ranks has 4 cards (one per suit), so:
- Total cards under a 4 = \( 2 \times 4 = 8 \)
- Probability = \( \frac{8}{52} = \frac{2}{13} \)

### Part (b): Probability of a card **above an 8**
Cards above an 8 are: 9, 10, Jack, Queen, King, and Ace. Each rank has 4 cards, so:
- Total cards above an 8 = \( 6 \times 4 = 24 \)
- Probability = \( \frac{24}{52} = \frac{6}{13} \)

### Part (c): Probability of a card **both under a 4 and above an 8**
The events "under a 4" and "above an 8" are mutually exclusive (they cannot happen at the same time). Therefore:
- Probability = \( 0 \)

### Part (d): Probability of a card **either under a 4 or above an 8**
We use the addition rule for probabilities:
- Probability(under a 4) = \( \frac{2}{13} \)
- Probability(above an 8) = \( \frac{6}{13} \)
- Since these two events are mutually exclusive, the probability of either event occurring is:
  \[
  \frac{2}{13} + \frac{6}{13} = \frac{8}{13}
  \]

### Summary of Answers
- (a) \( \frac{2}{13} \)
- (b) \( \frac{6}{13} \)
- (c) \( 0 \)
- (d) \( \frac{8}{13} \)

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### Related Questions
1. What is the probability of drawing a face card (Jack, Queen, or King) from the deck?
2. What is the probability of drawing a red card (hearts or diamonds)?
3. What is the probability of drawing a card that is either an Ace or a King?
4. How many ways can you draw a card that is a spade or a number less than 5?
5. What is the probability of drawing a card that is either black or an even number?

### Tip
When dealing with probabilities involving cards, always verify whether events are mutually exclusive to correctly apply the addition rule.

A card is dealt from a complete deck of fifty-two playing cards (no jokers). Use probability rules (when appropriate) to find the probability that the card is as stated. (Count an ace as high.)

Explore how to calculate the probabilities of drawing a card under 4, above 8, or either from a standard 52-card deck. This problem demonstrates probability concepts and rules for mutually exclusive events with step-by-step solutions. Ideal for students in Grades 9-12.

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