Find bag contains 4 white and 2 black balls .Another contains 3 white and 5 black balls .One ball is drawn from each bag .
Find the probability that both are white

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(1)/(4)`
D. `(3)/(4)`

Answer

To find the probability that both balls drawn from the two bags are white, we can follow these steps:

### Step 1: Identify the contents of the bags
- **Bag 1** contains 4 white balls and 2 black balls.
- **Bag 2** contains 3 white balls and 5 black balls.

### Step 2: Calculate the total number of balls in each bag
- For **Bag 1**: Total balls = 4 (white) + 2 (black) = 6 balls.
- For **Bag 2**: Total balls = 3 (white) + 5 (black) = 8 balls.

### Step 3: Calculate the probability of drawing a white ball from Bag 1
- **Favorable outcomes for Bag 1** (drawing a white ball) = 4.
- **Total outcomes for Bag 1** = 6.
- Probability of drawing a white ball from Bag 1, \( P(A) \) = Favorable outcomes / Total outcomes = \( \frac{4}{6} = \frac{2}{3} \).

### Step 4: Calculate the probability of drawing a white ball from Bag 2
- **Favorable outcomes for Bag 2** (drawing a white ball) = 3.
- **Total outcomes for Bag 2** = 8.
- Probability of drawing a white ball from Bag 2, \( P(B) \) = Favorable outcomes / Total outcomes = \( \frac{3}{8} \).

### Step 5: Calculate the combined probability that both balls drawn are white
Since the events of drawing a ball from Bag 1 and Bag 2 are independent, the combined probability \( P(A \cap B) \) is given by:
\[ P(A \cap B) = P(A) \times P(B) \]
Substituting the values we found:
\[ P(A \cap B) = \frac{2}{3} \times \frac{3}{8} \]

### Step 6: Simplify the expression
\[ P(A \cap B) = \frac{2 \times 3}{3 \times 8} = \frac{6}{24} = \frac{1}{4} \]

### Final Answer
The probability that both balls drawn are white is \( \frac{1}{4} \).

---