Question

try it!
jorge will flip two quarters at the same time. complete the tree diagram,
and then list the sample space of this compound event. use h for heads
and t for tails.
the sample space is:
convince me! how does the sample space change when the number
of quarters that jorge flips is increased by 1?

Explanation:

Step1: Fill tree diagram (Quarter1 H branch)

For Quarter 1 = H, Quarter 2 can be H or T. The empty box under H is $\text{T}$.

Step2: Fill tree diagram (Quarter1 lower branch)

Quarter 1's second possible outcome is $\text{T}$. For this branch, Quarter 2 can be H or T, so the empty box here is $\text{H}$.

Step3: List all sample space pairs

Combine each Quarter 1 outcome with matching Quarter 2 outcomes:

1. Quarter1=H, Quarter2=H: $\text{(H, H)}$
2. Quarter1=H, Quarter2=T: $\text{(H, T)}$
3. Quarter1=T, Quarter2=H: $\text{(T, H)}$
4. Quarter1=T, Quarter2=T: $\text{(T, T)}$

Step4: Analyze sample space size change

Original number of outcomes: $2^2=4$. Adding 1 quarter gives $2^3=8$ outcomes. The size doubles.

Answer:

Completed Tree Diagram Boxes (top to bottom, right column; left column bottom):

$\text{T}$, $\text{H}$, $\text{T}$

Sample Space:

$\{(H, H), (H, T), (T, H), (T, T)\}$

Convince Me! Response:

When the number of quarters is increased by 1, the size of the sample space doubles. Each existing outcome in the original sample space pairs with both heads (H) and tails (T) for the new quarter, so the total number of outcomes becomes $2 \times$ the original number of outcomes.