6. In a particular parliamentary constituency, the percentage of Conservative voters at the last election was \(35 \%\), and the percentage who voted for the Monster Raving Loony party was \(2 \%\).
- Find the probability that a random sample of 10 electors includes at least two Conservative voters.
Use suitable approximations to find
- the probability that a random sample of 500 electors will include at least 200 who voted either Conservative or Monster Raving Loony,
- the probability that a random sample of 200 electors will have at least 5 Monster Raving Loony voters in it.
- One of (b) or (c) requires an adjustment to be made before a calculation is done. Explain what this adjustment is, and why it is necessary.