9 Labrador puppies may be black, yellow or chocolate in colour. Some information about a litter of 9 puppies is given in the table.
| male | female |
| black | 1 | 3 |
| yellow | 2 | 1 |
| chocolate | 1 | 1 |
Four puppies are chosen at random to train as guide dogs.
- Determine the probability that exactly 3 females are chosen.
- Determine the probability that at least 3 black puppies are chosen.
- Determine the probability that exactly 3 females are chosen given that at least 3 black puppies are chosen.
- Explain whether the 2 events ‘choosing exactly 3 females’ and ‘choosing at least 3 black puppies’ are independent events.