Given: • P(A) = P(B) = P(C) = P(D) = k. • A and Care mutually exclusive • B and D are mutually exclusive. • A and B are independent. • A and D are independent. • B and C are independent. • C and D are independent. Find the largest possible value of k.

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Author:Amos Gilat
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# Probability Problem

**Given:**

- \( P(A) = P(B) = P(C) = P(D) = k \).
- \( A \) and \( C \) are mutually exclusive.
- \( B \) and \( D \) are mutually exclusive.
- \( A \) and \( B \) are independent.
- \( A \) and \( D \) are independent.
- \( B \) and \( C \) are independent.
- \( C \) and \( D \) are independent.

**Question:**
Find the largest possible value of \( k \).
Transcribed Image Text:# Probability Problem **Given:** - \( P(A) = P(B) = P(C) = P(D) = k \). - \( A \) and \( C \) are mutually exclusive. - \( B \) and \( D \) are mutually exclusive. - \( A \) and \( B \) are independent. - \( A \) and \( D \) are independent. - \( B \) and \( C \) are independent. - \( C \) and \( D \) are independent. **Question:** Find the largest possible value of \( k \).
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