Every morning, I roll a die to decide how to travel to work. If I roll a $1$ or $2$, I take
the train, if I roll a $3$, I catch a bus and otherwise I cycle. The probability that I am
late for work is $1/10$ if I travel by train, $1/5$ if I travel by bus and $1/20$ if I cycle.
I work a 5-day week.
I have worked out the probability i'm late to work is 11/120
(i) If I am late for work, what is the probablity that I travelled by train.
would this simple be $Pr(Travelled by Train | Late)$ hence $4/11$
(i) Calculate the probablity that I am on time every day during a week.
would this be $1-(11/120 * 5) $
(iii) I work for 46 weeks per year. Let Y denote the number of weeks in a year for which I am on time every day of the week. Find the mean and variance of Y .
Need help on this pleaseeeee.