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(F )

Options

A. `3/4`
B. `1/2`
C. `1/4`
D. `1/6`

Answer

To solve the problem, we need to find the probability of selecting the second bag (event F). Here’s a step-by-step solution:

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

### Step 2: Determine the probability of selecting each bag
Since one bag is selected at random from the two available bags, the probability of selecting either bag is equal.

### Step 3: Calculate the probability of selecting the second bag (event F)
The probability of selecting the second bag (F) can be calculated as follows:
- P(F) = Number of favorable outcomes for selecting the second bag / Total number of outcomes

Here, there is 1 favorable outcome (selecting the second bag) and 2 total outcomes (selecting either bag 1 or bag 2).

Thus, we have:
\[ P(F) = \frac{1}{2} \]

### Final Answer
The probability of selecting the second bag (event F) is:
\[ P(F) = \frac{1}{2} \]

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