given the experiment: draw 1 card from a standard 52 card deck, put the following events in order from 1 to 5. where 1 means it is the least likely to occur and 5 means the most likely to occur. Event k=draw a red 6. Event R= draw a heart face card. Event J - draw a jack of spades. Event F= draw a face card. Event h= draw a diamond

To determine the order of the events from least likely to most likely, we need to calculate the probability of each event occurring when drawing one card from a standard 52-card deck.

### Calculations:
1. **Event J (draw a jack of spades)**:
   - There is only **1 jack of spades** in a deck.
   - Probability \( P(J) = \frac{1}{52} \).

2. **Event k (draw a red 6)**:
   - There are **2 red 6s** (6 of hearts and 6 of diamonds).
   - Probability \( P(k) = \frac{2}{52} = \frac{1}{26} \).

3. **Event R (draw a heart face card)**:
   - There are **3 heart face cards** (jack, queen, king of hearts).
   - Probability \( P(R) = \frac{3}{52} \).

4. **Event h (draw a diamond)**:
   - There are **13 diamonds** in the deck.
   - Probability \( P(h) = \frac{13}{52} = \frac{1}{4} \).

5. **Event F (draw a face card)**:
   - There are **12 face cards** (3 face cards per suit: jack, queen, king).
   - Probability \( P(F) = \frac{12}{52} = \frac{3}{13} \).

### Order from Least Likely to Most Likely:
1. **Event J**: Draw a jack of spades \(\left(\frac{1}{52}\right)\).
2. **Event k**: Draw a red 6 \(\left(\frac{1}{26}\right)\).
3. **Event R**: Draw a heart face card \(\left(\frac{3}{52}\right)\).
4. **Event F**: Draw a face card \(\left(\frac{3}{13}\right)\).
5. **Event h**: Draw a diamond \(\left(\frac{1}{4}\right)\).

So, the order is: **J, k, R, F, h**.

Would you like more details or have any questions about these probabilities? Here are 8 related questions you might find interesting:

1. What is the probability of drawing a red face card?
2. How does the probability change if a card is drawn without replacement?
3. What is the probability of drawing a black card?
4. How likely is it to draw a 2 or a 3 from a standard deck?
5. What is the probability of drawing a king or an ace?
6. What is the probability of drawing a card that is both a diamond and a face card?
7. How does the probability of drawing a spade compare to drawing a diamond?
8. What is the probability of drawing a numbered card (2-10)?

**Tip:** When dealing with probabilities in card games, always start by identifying the total number of favorable outcomes relative to the total number of possible outcomes.

Explore how to determine the order of probabilities in drawing specific cards from a standard 52-card deck. This problem covers events such as drawing a jack of spades, a red 6, a heart face card, a face card, and a diamond. Suitable for students in Grades 9-12.

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