20. A large sack contains 1,000 flower seeds consisting of 300 carnations and 700 impatiens. Of the 300 carnation seeds, 200 will produce red flowers and 100 will produce white flowers. Of the 700 impatiens seeds, 400 will produce red flowers and 300 will produce white flowers.

a. If you randomly choose five seeds in succession

(without replacing any seeds that have been chosen), what is the probability that these seeds will produce two impatiens with red flowers, two carnations with red flowers, and one carnation with white flowers?

b. If you randomly choose four seeds in succession

(without replacing any seeds that have been chosen), what is the probability that these seeds will produce red- and white-flowered impatiens and red- and white-flowered carnations?

c. Given that four randomly chosen seeds all produce carnations, what is the probability that three are red flowered and one is white flowered?

d. Is the event of randomly choosing a carnation seed on the first draw independent of choosing an impatiens seed on the second draw?