A bag contains 3 red and 4 black balls and another bag has 4 red and 2 black balls . One bag is selected at random and from the selected at random and from the selected bag a ball is drawn .Let E be the event the first bag is selected F be the event that the second bag is selected ,G be the event that ball drawn is red .
find `P(E )`

Options

A. `1/2`
B. `3/4`
C. `1/4`
D. `5/8`

Answer

To find the probability of event E (the first bag being selected), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of bags:**
There are two bags in total:
- Bag 1: Contains 3 red balls and 4 black balls.
- Bag 2: Contains 4 red balls and 2 black balls.

2. **Determine the favorable outcomes for event E:**
Event E is defined as selecting the first bag. There is only one favorable outcome for this event, which is selecting Bag 1.

3. **Calculate the total outcomes:**
The total outcomes consist of selecting either Bag 1 or Bag 2. Thus, there are 2 total outcomes.

4. **Use the probability formula:**
The probability of an event is calculated using the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes for E}}{\text{Total number of outcomes}} \]
Substituting the values we identified:
\[ P(E) = \frac{1}{2} \]

5. **Final Answer:**
Therefore, the probability of selecting the first bag (event E) is:
\[ P(E) = \frac{1}{2} \]