In his closet, John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks. List all of the possible shirt-and-pant combinations below. John discovered that he also has a pair of boots and a pair of dress shoes in his closet. Make a tree diagram showing all of the possible shirt, pant, and shoe combinations.

During a bike challenge riders have to collect various colored ribbons each 1/2 mile they collect a red ribbon each eighth mile they collect a green ribbon and each quarter mile they collect a blue ribbion wich colors of ribion will be collected at the 3/4 markrer

An optical inspection system is used to distinguish among different part types. the probability of a correct classification of any part is 0.92. suppose that three parts are inspected and that the classifications are independent. let the random variable x denote the number of parts that are correctly classified. determine the probability mass function of x. round your answers to four decimal places (e. g. 98.7654). x f(x) 0 1 2 3

Find the maximum value of p= 4x + 5y subject to the following constraints :