A bag contains 5 red and 4 green balls and another bag contains 3 red and 7 black balls. If a ball is drawn from each bag. Find the probability that both are of different colours.

Options

A. `47/90`
B. `5/6`
C. `7/18`
D. `2/15`

Answer

To solve the problem, we need to find the probability that the balls drawn from each bag are of different colors. Let's break down the solution step by step.

### Step 1: Identify the total number of balls in each bag.
- **Bag 1** contains:
- 5 Red balls
- 4 Green balls
- Total = 5 + 4 = 9 balls

- **Bag 2** contains:
- 3 Red balls
- 7 Black balls
- Total = 3 + 7 = 10 balls

### Step 2: Determine the total outcomes when drawing one ball from each bag.
The total number of outcomes when drawing one ball from each bag is the product of the number of balls in both bags:
- Total outcomes = Total balls in Bag 1 × Total balls in Bag 2
- Total outcomes = 9 × 10 = 90

### Step 3: Calculate the favorable outcomes for drawing balls of different colors.
There are two scenarios where the balls drawn are of different colors:
1. A Red ball from Bag 1 and a Black ball from Bag 2.
2. A Green ball from Bag 1 and a Red ball from Bag 2.

#### Scenario 1: Red from Bag 1 and Black from Bag 2
- Number of ways to choose a Red ball from Bag 1 = 5
- Number of ways to choose a Black ball from Bag 2 = 7
- Total favorable outcomes for this scenario = 5 × 7 = 35

#### Scenario 2: Green from Bag 1 and Red from Bag 2
- Number of ways to choose a Green ball from Bag 1 = 4
- Number of ways to choose a Red ball from Bag 2 = 3
- Total favorable outcomes for this scenario = 4 × 3 = 12

### Step 4: Calculate the total favorable outcomes.
Total favorable outcomes = Outcomes from Scenario 1 + Outcomes from Scenario 2
- Total favorable outcomes = 35 + 12 = 47

### Step 5: Calculate the probability of drawing balls of different colors.
Probability = (Total favorable outcomes) / (Total outcomes)
- Probability = 47 / 90

### Final Answer:
The probability that both balls drawn are of different colors is **47/90**.

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