A dice is rolled. A card is drawn from a deck of face cards (i.e. obly jack, queen, king of each suit) A coun is flipped.
A) draw a tree diagram to define the sample space for this game.
The tree diagram for this game would look like this:
_____Dice (6 sides)_____
/ | \
Card Card Card
(4 face cards) (4 face cards) (4 face cards)
/ \ / \ / \
Heads Tails Heads Tails Heads Tails
(4 face cards) (4 face cards) (4 face cards)
In this diagram, the branches represent the possible outcomes of each event - rolling a dice, drawing a face card, and flipping a coin. The numbers in parentheses indicate the possible outcomes of each event (e.g., rolling a 6-sided dice has 6 possible outcomes, drawing a face card has 4 possible outcomes). The tree starts with the first event (rolling a dice), then branches out to the second event (drawing a face card), and finally branches out to the third event (flipping a coin).
To draw a tree diagram for this game, we can break it down into three separate events: rolling a dice, drawing a card, and flipping a coin.
Here's how the tree diagram would look:
1. Rolling a dice (6 possible outcomes):
- Outcome 1: Dice shows 1
- Outcome 2: Dice shows 2
- Outcome 3: Dice shows 3
- Outcome 4: Dice shows 4
- Outcome 5: Dice shows 5
- Outcome 6: Dice shows 6
2. Drawing a card (12 possible outcomes):
- Outcome 1: Drawing a Jack of Hearts
- Outcome 2: Drawing a Jack of Diamonds
- Outcome 3: Drawing a Jack of Clubs
- Outcome 4: Drawing a Jack of Spades
- Outcome 5: Drawing a Queen of Hearts
- Outcome 6: Drawing a Queen of Diamonds
- Outcome 7: Drawing a Queen of Clubs
- Outcome 8: Drawing a Queen of Spades
- Outcome 9: Drawing a King of Hearts
- Outcome 10: Drawing a King of Diamonds
- Outcome 11: Drawing a King of Clubs
- Outcome 12: Drawing a King of Spades
3. Flipping a coin (2 possible outcomes):
- Outcome 1: Coin shows heads
- Outcome 2: Coin shows tails
To determine the complete sample space, combine all three events and their respective outcomes. Each unique path in the tree diagram represents a possible combination of events.
Please note that since no probabilities or restrictions are mentioned, all outcomes are assumed to have an equal chance of occurring.