To solve the problem, we need to analyze both quantities step by step.
### Step 1: Calculate the probability of contradiction between X and Y (Quantity I)
1. **Probability of X telling the truth**:
\[
P(X \text{ truth}) = 35\% = \frac{35}{100} = 0.35
\]
2. **Probability of Y telling the truth**:
\[
P(Y \text{ truth}) = 75\% = \frac{75}{100} = 0.75
\]
3. **Probability of X telling a lie**:
\[
P(X \text{ lie}) = 1 - P(X \text{ truth}) = 1 - 0.35 = 0.65
\]
4. **Probability of Y telling a lie**:
\[
P(Y \text{ lie}) = 1 - P(Y \text{ truth}) = 1 - 0.75 = 0.25
\]
5. **Probability of contradiction**: There are two scenarios for contradiction:
- X tells the truth and Y tells a lie.
- X tells a lie and Y tells the truth.
Therefore, the total probability of contradiction is:
\[
P(\text{contradiction}) = P(X \text{ truth}) \times P(Y \text{ lie}) + P(X \text{ lie}) \times P(Y \text{ truth})
\]
Substituting the values:
\[
P(\text{contradiction}) = (0.35 \times 0.25) + (0.65 \times 0.75)
\]
\[
= 0.0875 + 0.4875 = 0.575
\]
### Step 2: Calculate the probability of getting an even sum when two dice are thrown (Quantity II)
1. **Total outcomes when two dice are thrown**:
\[
\text{Total outcomes} = 6 \times 6 = 36
\]
2. **Favorable outcomes for even sums**:
The sums that can be even are 2, 4, 6, 8, 10, and 12. The combinations that yield these sums are:
- Sum = 2: (1,1)
- Sum = 4: (1,3), (2,2), (3,1)
- Sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1)
- Sum = 8: (2,6), (3,5), (4,4), (5,3), (6,2)
- Sum = 10: (4,6), (5,5), (6,4)
- Sum = 12: (6,6)
Counting these combinations:
- For sum = 2: 1 way
- For sum = 4: 3 ways
- For sum = 6: 5 ways
- For sum = 8: 5 ways
- For sum = 10: 3 ways
- For sum = 12: 1 way
Total favorable outcomes = 1 + 3 + 5 + 5 + 3 + 1 = 18
3. **Probability of getting an even sum**:
\[
P(\text{even sum}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{18}{36} = \frac{1}{2} = 0.5
\]
### Step 3: Compare the two quantities
- Quantity I (probability of contradiction): 0.575
- Quantity II (probability of even sum): 0.5
Since 0.575 > 0.5, we conclude that:
**Quantity I is greater than Quantity II.**
### Final Answer:
**Quantity I > Quantity II**
