Problem 19E

Randomization in a study of TV commercials. Gonzaga University professors conducted a study of more than 1,500 television commercials and published their results in the Journal of Sociology, Social Work and Social Welfare (Vol. 2, 2008). Commercials from eight networks—ABC, FAM, FOX, MTV, ESPN, CBS, CNN, and NBC—were sampled during an 8-day period, with one network randomly selected each day. The table below shows the actual order determined by random draw:

a. What is the probability that ESPN was selected on Monday, July 11?

b. Consider the four networks chosen for the weekends (Saturday and Sunday). How many ways could the researchers select four networks from the eight for the weekend analysis of commercials? (Assume that the order of assignment for the four weekend days was immaterial to the analysis.)

c. Knowing that the networks were selected at random, what is the probability that ESPN was one of the four networks selected for the weekend analysis of commercials?

Answer

Step 1 of 3

(a)

Eight commercials networks were sampled during an 8-day period, with one network randomly selected each day.

The table below shows the actual order determined by random draw:

Networks |
Day |

ABC |
July 6 (Wed) |

FAM |
July 7 (Thr) |

FOX |
July 9 (Sat) |

MTV |
July 10 (Sun) |

ESPN |
July 11 (Mon) |

CBS |
July 12 (Tue) |

CNN |
July 16 (Sat) |

NBC |
July 17 (Sun) |

We are asked to find the probability that ESPN was selected on Monday, July 11.

One can select any networks during an 8-day period, hence the probability that any network is selected on a particular day is

Hence the probability that ESPN was selected on Monday, July 11 is