Discrete Random Variables (DRV)

Over a long period of time, \(4\) out of \(7\) customers use credit card to purchase goods at a supermarket. If a sample of \(15\) customers are selected at random, determine the probability that

1. More than \(7\) customers use credit card to purchase goods.
2. More than \(7\) customers use credit card to purchase goods given that at most \(10\) of them use credit card to purchase goods.
3. At least \(5\) of the samples have at most \(6\) customers use credit card to purchase goods, given that \(20\) such samples are taken.