Question

Monitor three consecutive phone calls going through a telephone switching office. Classify each one as a voice call (v) if someone is speaking, or a data call (d) if the call is carrying a modem or fax signal. Your observation is a sequence of three letters (each letter is eitherv or d). For example, two voice calls followed by one data call corresponds to vvd. Write the elements of the following sets: (1) A1 ={first call is a voice call} (2) B1 ={first call is a data call} (3) A2 ={second call is a voice call} (4) B2 ={second call is a data call} (5) A3 ={all calls are the same} (6) B3 ={voice and data alternate} (7) A4 ={one or more voice calls} (8) B4 ={two or more data calls} For each pair of events A1 and B1,A 2 and B2, andso on, identify whether the pair of events is either mutually exclusive or collectively exhaustive or both.

Answer 1

A1 = { vvv , vvd , vdd, vdv }

B1 = { ddd, dvv, dvd, ddv }

A2 = { vvv, vvd, dvd, dvv}

B2 ={ ddd, vdv, vdd, ddv}

A3 = { vvv, ddd}

B3 = { vdv, dvd }

A4 = { vdd, dvd, ddv, vvd, vdv, dvv, vvv}

B4= { ddv, dvd, vdd, ddd }

A1 and B1 are mutually exclusive and collectively exhaustive.

A2 and B2 are mutually exclusive and collectively exhaustive.

A3 and B3 are mutually exhaustive but are not collectively exhaustive

A4 and B4 are not mutually exclusive but are collectively exhaustive.