2 An ordinary fair die is thrown until a 6 is obtained.
- Find the probability that obtaining a 6 takes more than 8 throws.
Two ordinary fair dice are thrown together until a pair of 6s is obtained. The number of throws taken is denoted by the random variable \(X\). - Find the expected value of \(X\).
- Find the probability that obtaining a pair of 6s takes either 10 or 11 throws.