91Ó°ÊÓ

A large jet aircraft has two wheels per landing gear for added safety. The tires are rated so that even with a "hard landing" the probability of any single tire blowing out is only \(0.10\). (a) What is the probability that a landing gear (with two tires) will survive even a hard landing with at least one good tire? (b) In order for the plane to land safely, all three landing gears (the nose and both wing landing gears) must have at least one good tire. What is the probability that the jet will be able to land safely even on a hard landing?

In the game of pinochle the deck consists of 48 cards - two each of the 9,10, jack, queen, king, and ace for each of the four suits. There are four players and each is dealt 12 cards. What is the probability a given player is dealt four kings (one of each suit), four queens (one of each suit), and four other cards none of which is a king or queen? (Such a hand is referred to as a bare roundhouse.)

A fair die is rolled three times and the random variable \(X\) records the number of different outcomes that result. For example, if two 5 's and one 4 are rolled, then \(X\) records two different outcomes. Determine (a) the probability distribution for \(X\); (b) \(E(X)\); and (c) \(\operatorname{Var}(X)\).