3 A factory makes a large number of ropes with lengths either 3 m or 5 m . There are four times as many ropes of length 3 m as there are ropes of length 5 m .
- One rope is chosen at random. Find the expectation and variance of its length.
- Two ropes are chosen at random. Find the probability that they have different lengths.
- Three ropes are chosen at random. Find the probability that their total length is 11 m .