Answer: 0.58.

## Explanation Bayes' formula states: \[ P(X|I) = \frac{P(I|X) \times P(X)}{P(I)} \] Where: - \( P(X|I) \) = Updated probability of X given the new information - \( P(I|X) \) = Probability of the new information given X = 0.50 - \( P(X) \) = Prior probability of X = 0.70 - \( P(I) \) = Unconditional probability of the new information = 0.60 Plugging in the values: \[ P(X|I) = \frac{0.50 \times 0.70}{0.60} = \frac{0.35}{0.60} = 0.5833 \] Rounded to two decimal places, this is approximately 0.58. **Step-by-step calculation:** 1. Multiply \( P(I|X) \) and \( P(X) \): \( 0.50 \times 0.70 = 0.35 \) 2. Divide by \( P(I) \): \( 0.35 \div 0.60 = 0.5833 \) 3. The result is closest to 0.58 (Option B) **Why not the other options?** - **Option A (0.43)**: This would be \( \frac{0.50 \times 0.70}{0.80} \) or similar incorrect calculation - **Option C (0.84)**: This would be \( \frac{0.60 \times 0.70}{0.50} \) or similar incorrect calculation **Key Concept**: Bayes' theorem allows us to update prior probabilities with new information to obtain posterior probabilities, which is fundamental in probability theory and statistical inference.

Author: LeetQuiz .