Multiplication Theorem On Probability

Step 1: Understanding the Concept:
Total balls . Use the multiplication rule of probability for dependent events (without replacement).

Step 2: Detailed Explanation:
After removing 1 white, 34 balls remain, of which 17 are black:


Step 3: Final Answer:
The required probability is .

Step 1: Express real and imaginary parts.
We are given: Let , where and .
Step 2: Simplify the equation.
First, simplify by multiplying the numerator and denominator by the complex conjugate of the denominator : Now, simplify the left-hand side: Multiply the first term by and the second term by to rationalize: This simplifies to:
Step 3: Equate real and imaginary parts.
Equating real and imaginary parts gives the system of equations: Solving these equations, we find: Multiplying the second equation by 2: Now adding the equations: Substitute into : Thus, the locus of is .
Final Answer: .