7 A shop sells old video tapes, of which 1 in 5 on average are known to be damaged.
- A random sample of 15 tapes is taken. Find the probability that at most 2 are damaged.
- Find the smallest value of \(n\) if there is a probability of at least 0.85 that a random sample of \(n\) tapes contains at least one damaged tape.
- A random sample of 1600 tapes is taken. Use a suitable approximation to find the probability that there are at least 290 damaged tapes.