Question: A large number of seeds from a certain species of flower are collected and mixed together in the following proportions according to the color of the flowers they will produce: 2 red, 2 white, 1 blue. If these seeds are mixed and then randomly packaged in bags containing about 100 seeds, what is the probability that a bag will contain the following:

a. At most 50% of white seeds?

b. At least 65 seeds that are not "white"?

c. At least 25 but at most 45 "white" seed?

d. Within what limits would you expect the number of white seeds to lie with probability .95?

Thank you!  Edit

Answer: In binomial experiment we know,
P(x=i) = nCi p^i q^(n - i)

Here, n = 100, p = 0.4, q = 1 - p = 0.6

a. At most 50% = P(x ≤ 50) =P(x=0)+P(x=1)+....+P(x=50)
=(100C0*0.4^0*0.6^100)+(100C1*0.4^1*0.…
= 0.9832

b. At least 65 not white means P(x ≤ 35)
=P(x=0)+P(x=1)+....+P(x=35)
=(100C0*0.4^0*0.6^100)+(100C1*1.4^1*0.…
= 0.1795  Edit