In a shipment of 15 room air conditioners , there are 3 with defective thermostat. Two air conditioners will be selected at random and inspected. Find the probability thatA) the first is defectiveB) both are defectiveC) exactly one is defective.

Of the cartons produced by a company, 10% have a puncture, 5% have a smashed corner, and 0.9% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner (Type an integer or a decimal. Do not round.)

A college surveys the 1258 alumni from 2019 and 2020. Of the 679 alumni from 2019, 127 went on to graduate school. Of the 579 alumni from 2020, 196 went on to graduate school. Find the probability that an alumnus selected at random from 2019 and 2020 is as described. a) a 2019 alumnus? b) a 2020 alumnus? c) a 2019 alumnus who did not attend graduate school?

Five people, designated as A,AB,C,D,E are arranged in linear order. Assuming that each possible order is equally likely, what is the probability that there are exactly two people between A and B?