Probability

Need some help with this:

Let Y denote the number of weeks in a year for which I am on time every day of the week. Find mean and variance of Y.

I found out the probabilities asked before (prob. of being on time every day)

Need some help with this:

Let Y denote the number of weeks in a year for which I am on time every day of the week. Find mean and variance of Y.

I found out the probabilities asked before (prob. of being on time every day)

I don't understand the last line. Can you post the full question pls.

Every morning I roll a fair die to decide how I travel to work. The question specifies the probability that the person cycles, bus, or train, and the probability of being late/on time. The first 3 parts asked me to find the prob. of being late, probability of taking the train given being late, and prob. of being on time every day (the person works 5 days).

The last part is what I'm having trouble with. The person works 46 weeks a year. Let Y denote the no. of weeks in a year for which they're on time every day of the week. Find mean and variance of Y. That's all the info I've been given.

There is a fixed number of 'trials', those are the 46 weeks in each of which they can be on time every day, or not.
There are two possible outcomes: on time every day of the week, or not.
It's implied that the probability of being on time every day of the week is a fixed probability.
It's reasonable to assume that one week's outcome doesn't affect the next week's outcome (independence).
So Y satisfies the requirements of a binomial probability distribution.

Oh right. Would I be right in saying the mean = np and the variance is np(1-p)?