To find the probability that both balls drawn from Jar I and Jar II are blue, we first need to determine the total number of balls in each jar.
Jar I:
- Blue balls: 3
- Yellow balls: 4
- Total balls in Jar I = 3 + 4 = 7
Jar II:
- Blue balls: 5
- Yellow balls: 6
- Total balls in Jar II = 5 + 6 = 11
Next, we calculate the probability of drawing a blue ball from each jar.
Probability of drawing a blue ball from Jar I: \[ P(\text{Blue from Jar I}) = \frac{\text{Number of blue balls in Jar I}}{\text{Total number of balls in Jar I}} = \frac{3}{7} \]
Probability of drawing a blue ball from Jar II: \[ P(\text{Blue from Jar II}) = \frac{\text{Number of blue balls in Jar II}}{\text{Total number of balls in Jar II}} = \frac{5}{11} \]
Now we need to find the probability that both events occur (drawing a blue ball from both jars). Since these events are independent, we multiply the probabilities:
\[ P(\text{Both balls are blue}) = P(\text{Blue from Jar I}) \times P(\text{Blue from Jar II}) = \frac{3}{7} \times \frac{5}{11} \]
Calculating this gives:
\[ P(\text{Both balls are blue}) = \frac{3 \times 5}{7 \times 11} = \frac{15}{77} \]
Thus, the probability that both balls drawn are blue is:
\[ \boxed{\frac{15}{77}} \]