There are 8 white and 7 black balls in first bag and 9 white and 6 black balls are in second bag. One ball is drawn from each bag. Find the probability that both are of the same colour.

Explanation

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

### Step 1: Determine the total number of balls in each bag
- **First Bag**: 8 white balls + 7 black balls = 15 balls
- **Second Bag**: 9 white balls + 6 black balls = 15 balls

### Step 2: Calculate the probability of drawing a white ball from both bags
- Probability of drawing a white ball from the first bag:
\[ P(\text{White from Bag 1}) = \frac{8}{15} \]
- Probability of drawing a white ball from the second bag:
\[ P(\text{White from Bag 2}) = \frac{9}{15} \]
- Therefore, the probability of both balls being white is:
\[ P(\text{Both White}) = P(\text{White from Bag 1}) \times P(\text{White from Bag 2}) = \frac{8}{15} \times \frac{9}{15} = \frac{72}{225} \]

### Step 3: Calculate the probability of drawing a black ball from both bags
- Probability of drawing a black ball from the first bag:
\[ P(\text{Black from Bag 1}) = \frac{7}{15} \]
- Probability of drawing a black ball from the second bag:
\[ P(\text{Black from Bag 2}) = \frac{6}{15} \]
- Therefore, the probability of both balls being black is:
\[ P(\text{Both Black}) = P(\text{Black from Bag 1}) \times P(\text{Black from Bag 2}) = \frac{7}{15} \times \frac{6}{15} = \frac{42}{225} \]

### Step 4: Add the probabilities of both events
Since the events (both balls being white and both balls being black) are mutually exclusive, we can add their probabilities:
\[ P(\text{Both Same Color}) = P(\text{Both White}) + P(\text{Both Black}) = \frac{72}{225} + \frac{42}{225} = \frac{114}{225} \]

### Step 5: Simplify the final probability
To simplify \(\frac{114}{225}\):
- The greatest common divisor of 114 and 225 is 3.
- Dividing both the numerator and the denominator by 3:
\[ \frac{114 \div 3}{225 \div 3} = \frac{38}{75} \]

### Final Answer
The probability that both balls drawn are of the same color is:
\[ \frac{38}{75} \]