Question 1193749
### (a) Approximation of \( P(B) \)

To approximate \( P(B) \), divide the observed frequency of \( B \) by the total number of runs. 

\[
P(B) = \frac{\text{Frequency of } B}{\text{Total Runs}}
\]

Where:
- Frequency of \( B = 2322 \),
- Total runs = \( 2322 + 2360 + 5318 = 10000 \).

Substitute values:

\[
P(B) = \frac{2322}{10000} = 0.2322
\]

### (b) Best Approximation of \( P(C) \)

It is given that \( P(C) = P(D) \). Since the frequencies of \( C \) and \( D \) are 2360 and 5318 respectively, the best way to approximate \( P(C) \) and \( P(D) \) is to split the combined probability equally between them. 

#### Step 1: Find \( P(C) + P(D) \)

The combined probability of \( C \) and \( D \) is:

\[
P(C) + P(D) = \frac{\text{Frequency of } C + \text{Frequency of } D}{\text{Total Runs}}
\]

Substitute values:

\[
P(C) + P(D) = \frac{2360 + 5318}{10000} = \frac{7678}{10000} = 0.7678
\]

#### Step 2: Split Equally Between \( P(C) \) and \( P(D) \)

Since \( P(C) = P(D) \):

\[
P(C) = P(D) = \frac{P(C) + P(D)}{2} = \frac{0.7678}{2} = 0.3839
\]

### Final Answers:
(a) \( P(B) = 0.2322 \)  
(b) \( P(C) = 0.3839 \)