3. For a particular type of plant \(45 \%\) have white flowers and the remainder have coloured flowers. Gardenmania sells plants in batches of 12. A batch is selected at random.
Calculate the probability that this batch contains
- exactly 5 plants with white flowers,
- more plants with white flowers than coloured ones.
Gardenmania takes a random sample of 10 batches of plants.
- Find the probability that exactly 3 of these batches contain more plants with white flowers than coloured ones.
Due to an increasing demand for these plants by large companies, Gardenmania decides to sell them in batches of 50 .
- Use a suitable approximation to calculate the probability that a batch of 50 plants contains more than 25 plants with white flowers.