Question

Three women A, B and C share an office with one telephone. Calls for this office arrive at random during working hours in the ratios 3,2,1 for A, B and C respectively. Because of the nature of their work the three women leave the office independently at random times, so that A is absent 1/5 of her working hours and B and C are each absent 1/4 of their working hours. On occasions where the telephone rings during office hours find the probabilities that:

(i) no one is in the office to answer the phone

(ii) a caller who wishes to speak to C is able to do so

(iii) a caller cannot speak to the person he wishes to contact

(iv) a caller who wishes to speak to B is unable to on three consecutive occasions

(v) three successive calls are all for different people

(vi) given that two consecutive calls are for the same person, they are both for C

Answer 1

the probability that during working hours call arrive for A is

the probability that during working hours call arrive for B is

the probability that during working hours call arrive for C is

i)probability that no one is there to answer the call = The probability that A and B and C is absent.

=

ii)probability that a caller who wishes to speak to C is able to do so = probability that the call arrives for C and C is not absent =

iii) probability that a caller cannot speak to the person he wishes to contact = probability that call arrives for A and A is absent or call arrives for B and B is absent or call arrives for C and C is absent

=

iv)probability that caller wishes to speak to B and cannot =

a caller who wishes to speak to B is unable to on three consecutive occasions =