10. Consider the game where two dice, die A and die B, are rolled. We say that die A wins, and write A :> B, if the outcome of rolling A is larger than that of rolling B. If both rolls result in the same number it is a tie. (a) Find the probability of a tie. (b) Find the probability that die A wins. 12. Seventy percent of the light aircraft that disappear while in ight in a certain country are subsequently dis- covered. Of the aircraft that are discovered, 60% have an emergency locator, whereas 10% of the aircraft not discovered have such a locator. Suppose a light aircraft disappears while in ight. (a) What is the probability that it has an emergency locator and it will not be discovered? (b) What is the probability that it has an emergency locator? (c) If it has an emergency locator, what is the probability that it will not be discovered