4. Patrick is practising his skateboarding skills. On each day, he has 30 attempts at performing a difficult trick. Every time he attempts the trick, there is a probability of 0.2 that he will fall off his skateboard.
Assume that the number of times he falls off on any given day may be modelled by a binomial distribution.

1. 1. Find the mean number of times he falls off in a day.
2. (ii) Find the variance of the number of times he falls off in a day.
3. 1. Find the probability that, on a particular day, he falls off exactly 10 times.
4. (ii) Find the probability that, on a particular day, he falls off 5 or more times.
5. Patrick has 30 attempts to perform the trick on each of 5 consecutive days.
6. 1. Calculate the probability that he will fall off his skateboard at least 5 times on each of the 5 days.
7. (ii) Explain why it may be unrealistic to use the same value of 0.2 for the probability of falling off for all 5 days.