The archery tournament:

At an archery tournament, eight of the twenty competitors were left-handed and the remainders were right-handed.

1. Find the probability that an archer chosen at random is left-handed.

2. If a pair of archers is chosen at random is left-handed. Find the probability that exactly one of the pair is left-handed.

Due to the weather conditions it is more difficult for left-handers to hit the target. Practice sessions indicated that the probability of a left-hander hitting the target was 0.7, while for right-hander it was 0.9.

3. Find the probability that an archer chosen at random is left-handed and hits the target.

4. Find the probability that an archer chosen at random hits the target.

5. If an archer hits the target, find the probability that the person was right-handed.

6. Fin the probability that two archers chosen at random are the same hand and both hit the target.

7. Draw up a table which shows the probability for each outcome possible for two randomly chosen arches.