A bag contains 4 white and 5 blue balls another bag contains 5 white 7 blue balls what is probability of choosing two balls one from each bag such that one is white and other is blue?

Options

A. 15/78
B. 25/67
C. (11/45)
D. 53/108

Answer

To solve the problem of finding the probability of choosing two balls, one from each bag, such that one is white and the other is blue, we can follow these steps:

### Step 1: Identify the contents of each bag
- **Bag 1** contains 4 white balls and 5 blue balls.
- **Bag 2** contains 5 white balls and 7 blue balls.

### Step 2: Calculate the total number of balls in each bag
- Total balls in Bag 1 = 4 (white) + 5 (blue) = 9 balls.
- Total balls in Bag 2 = 5 (white) + 7 (blue) = 12 balls.

### Step 3: Calculate the probabilities for each case
We need to consider two cases for selecting one white ball and one blue ball:

#### Case 1: White ball from Bag 1 and blue ball from Bag 2
- Probability of choosing a white ball from Bag 1 = Number of white balls in Bag 1 / Total balls in Bag 1 = 4/9.
- Probability of choosing a blue ball from Bag 2 = Number of blue balls in Bag 2 / Total balls in Bag 2 = 7/12.
- Combined probability for this case = (4/9) * (7/12).

#### Case 2: Blue ball from Bag 1 and white ball from Bag 2
- Probability of choosing a blue ball from Bag 1 = Number of blue balls in Bag 1 / Total balls in Bag 1 = 5/9.
- Probability of choosing a white ball from Bag 2 = Number of white balls in Bag 2 / Total balls in Bag 2 = 5/12.
- Combined probability for this case = (5/9) * (5/12).

### Step 4: Calculate the total probability
Now we add the probabilities from both cases:
1. Probability from Case 1 = (4/9) * (7/12) = 28/108.
2. Probability from Case 2 = (5/9) * (5/12) = 25/108.

Total probability = (28/108) + (25/108) = (28 + 25) / 108 = 53/108.

### Step 5: Final answer
The probability of choosing one white ball and one blue ball is **53/108**.

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