Paul checks the weather forecast. If the forecast is good, Paul will go out for a walk. If the forecast is bad, then Paul will either stay home or go out. If he goes out, he might either remember or forget his umbrella. In the tree diagram below, identify the leaf that corresponds to the event that the forecast is bad and Paul stays home.
1. goes for a walk
2. doesn't go
3. remember his umbrella
4. forgets his umbrella
So, 2nd.
no diagram
To identify the leaf that corresponds to the event that the forecast is bad and Paul stays home, we need to follow the tree diagram provided. Let's analyze the options step-by-step:
- Start with the top node of the diagram, which represents checking the weather forecast.
- Move down to the next level, where we have two branches: "Good Forecast" and "Bad Forecast."
- Since we are looking for the event where the forecast is bad, we follow the branch that corresponds to the "Bad Forecast."
- Now we are at the next level, where we have two more branches: "Stay Home" and "Go Out."
- We are interested in the event where Paul stays home, so we follow the "Stay Home" branch.
Thus, the leaf that corresponds to the event that the forecast is bad and Paul stays home is located at the end of the "Bad Forecast" branch and the "Stay Home" branch.
To identify the leaf that corresponds to the event that the forecast is bad and Paul stays home, we can use the given information to draw a tree diagram.
First, let's identify the possible outcomes at each step:
1. Weather forecast: Good or Bad.
2. Paul's decision: Go out or Stay home.
3. If Paul goes out: Remember umbrella or Forget umbrella.
Now, let's draw the tree diagram:
Weather Forecast
/ \
Good Bad
/ \ / \
Go out Stay home Go out Stay home
/ \ / \
Remember Forget Remember Stay home
umbrella umbrella umbrella
From the tree diagram, we can see that the leaf that corresponds to the event that the forecast is bad and Paul stays home is the "Stay home" leaf under the "Bad" branch of the "Weather Forecast" node.
Therefore, the leaf that corresponds to the event that the forecast is bad and Paul stays home is "Stay home" under the "Bad" branch.