Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) = 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 1000 randomly chosen plants from this species and finds the following distribution of traits: open 3 leaves N3,open 5 leaves N5,open closed N3, closed N5,closed a) Assuming the two traits are independent, determine the expectations of the counts N3,open, N3,closed, N5,open, and N5,closed in the table. b) Determine an approximate value for the probability P(N3,open > 340).

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