Let denote the event that the man is ill, and denote the event that his wife is ill.Originally Posted by Natasha
Then the probability of the event that he is off work is:
this means that the probability is the sum of the probabilities of the
sub-events minus the probability that both sub-events occur (this is
because this is included within both sub-events will be double counted
if we do not subtract one of it).
Think of it like this: In 1000 days the man is ill on 50 days, his wife is ill
20 days, both are ill on 5 days, so he is off 50+20-5 days(this last to remove
double counted days)
2) Find the conditional probability that he is ill given his wife is? Compare this with the corresponding unconditional probability: does it seem reasonable?
where denotes the probability that event occurs given that event occurs so:
Which is reasonable. It tell us that if his wife is ill he is more likely
to be ill also.
(Of the 20 days in 1000 that his wife is ill he is also ill on 5 of the days)
In a thousand days he is off work for 65 days, of which he is ill on3) If you know he is off work, what is the probability he is ill?