4. Michael works for a new small company, DataInfo, but has been ill recently. It
is Sunday, and Michael's manager thinks the probabilities that Michael will be
well enough to attend work on each of the next three (assumed independent) days
are given by 0.2, 0.3 and 0.4 respectively. Michael's son Hugh is also ill and has
probability of 0.7 of being ill on each of the next three days. The manager thinks
that probability that both Michael and Hugh will be ill on the same day is 0.5.
(a) Are these probabilities personal probabilities or relative frequency probabili-
ties? Explain your answer.
[3]
(b) What is the probability that Michael will not be able to attend work on Monday
and Tuesday?
[3]
(c) Given that Michael is able to attend on Monday, what is the probability that
he will attend on Tuesday?
[2]
(d) Event A occurs if Michael is ill on Monday. Event B occurs if Hugh is ill on
Monday. Are A and B mutually exclusive events? Explain your answer. [2]
(e) It is Wednesday morning and Hugh is sick. What is the probability that Michael
will not be able to attend work?
[5]