Question

Two jars each contain blue balls and yellow balls. JarI contains 3 blue balls and 4 yellow balls and Jar II contains 5 blue balls and 6 yellow balls. A ball is drawn from each jar. What is the probability that both balls are blue?

A.
8/77

B.
10/77

C.
15/77

D.
24/77

Answer 1

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:

\[
\boxed{\frac{15}{77}}
\]