Total number of Caps in a bag, which contains While and Black Cup only, is 16. What is the number of White Cap?
(A) Probability of drawing a White Caps p (W) `lt` 0.3750
(B) Probability of drawing two Black Caps `P(B) lt1-P(W)`
(C ) Difference between no. of White Caps and Black Caps is 12.

Options

A. Only statement 'A' alone is suffiecient to answer the question.
B. Both statement A and statement C are required to answer the question.
C. Only statement 'C' alone is sufficient to answer the question
D. Wither statemetn A or statement C is sufficient to answer the question

Explanation

To solve the problem, we need to determine the number of white caps in a bag containing both white and black caps, given the following information:

1. The total number of caps (white and black) is 16.
2. The probability of drawing a white cap \( P(W) < 0.3750 \).
3. The difference between the number of white caps and black caps is 12.

Let's denote:
- \( W \) = number of white caps
- \( B \) = number of black caps

### Step 1: Set Up the Equations
From the information provided, we can set up the following equations:

1. The total number of caps:
\[ W + B = 16 \quad \text{(1)} \]

2. The difference between the number of white caps and black caps:
\[ |W - B| = 12 \quad \text{(2)} \]

### Step 2: Solve for \( W \) and \( B \)
From equation (2), we have two possible cases:
- Case 1: \( W - B = 12 \)
- Case 2: \( B - W = 12 \)

#### Case 1: \( W - B = 12 \)
From this, we can express \( W \) in terms of \( B \):
\[ W = B + 12 \quad \text{(3)} \]
Substituting equation (3) into equation (1):
\[ (B + 12) + B = 16 \]
\[ 2B + 12 = 16 \]
\[ 2B = 4 \]
\[ B = 2 \]
Now substituting \( B = 2 \) back into equation (3):
\[ W = 2 + 12 = 14 \]

#### Case 2: \( B - W = 12 \)
From this, we can express \( B \) in terms of \( W \):
\[ B = W + 12 \quad \text{(4)} \]
Substituting equation (4) into equation (1):
\[ W + (W + 12) = 16 \]
\[ 2W + 12 = 16 \]
\[ 2W = 4 \]
\[ W = 2 \]
Now substituting \( W = 2 \) back into equation (4):
\[ B = 2 + 12 = 14 \]

### Step 3: Analyze the Results
From the two cases, we have:
- Case 1: \( W = 14 \) and \( B = 2 \)
- Case 2: \( W = 2 \) and \( B = 14 \)

### Step 4: Check the Probability Condition
Now we need to check the probability condition \( P(W) < 0.3750 \):
- The total number of caps is 16.
- The probability of drawing a white cap is given by:
\[ P(W) = \frac{W}{W + B} = \frac{W}{16} \]

For Case 1:
\[ P(W) = \frac{14}{16} = 0.875 \quad \text{(not valid)} \]

For Case 2:
\[ P(W) = \frac{2}{16} = 0.125 \quad \text{(valid)} \]

### Conclusion
The only valid case that satisfies all conditions is Case 2, where:
- Number of White Caps \( W = 2 \)
- Number of Black Caps \( B = 14 \)

Thus, the number of white caps is **2**.