Mathematics
Mathematics
Problem
A fair die is thrown three times. What is the probability that exactly two sixes appear? a) b) c) d)Intuitive explanation
This is a binomial probability problem: you have a fixed number of independent trials (three rolls), each with the same success probability (rolling a six), and you want exactly a certain number of successes. The key is to count both the ways to choose which two rolls show sixes and the probability of each outcome—then multiply by the number of arrangements. Think of it as: "In how many positions can I place my two sixes, and what's the probability of each arrangement?"
Intuitive explanation
This is a binomial probability problem: you have a fixed number of independent trials (three rolls), each with the same success probability (rolling a six), and you want exactly a certain number of successes. The key is to count both the ways to choose which two rolls show sixes and the probability of each outcome—then multiply by the number of arrangements. Think of it as: "In how many positions can I place my two sixes, and what's the probability of each arrangement?"