Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is:
Step-by-Step Solution
Key Concept: This is a conditional probability problem requiring careful application of inclusion-exclusion principle. Given that two specific outcomes (5 and 6) have appeared on two dice, we must calculate P(4 and 3 on remaining dice | 5 and 6 on two dice) by finding the reduced sample space where at least one die shows 5 and at least one shows 6.
When 5 and 6 appear on two dice, the sample space reduces to $6^4 - 2 imes 5^4 + 4^4$ by inclusion-exclusion. With 24 favorable outcomes, the probability is $ rac{24}{302} = rac{12}{151}$.
Correct Answer: 3