6. In a fruit packing plant, apples are packed on to trays of 10 , and then checked for blemishes. The chance of any particular apple having a blemish is \(5 \%\). If a tray is selected at random, find
- the probability that at least two of the apples in it are blemished,
- the probability that exactly two are blemished.
Trays are now packed in boxes of 50 trays each. In one such box, find
- the probability that at most one tray contains at least two blemished apples,
- the expected number of trays containing at least two blemished apples.
- Use a suitable approximation to find the probability that in a random selection of 20 trays there are more than 10 blemished apples.