HELP! P with percentages...3 problems

[mathmoron]

1. A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this populatin prefers the color red. If 20 buyers are randomly selected, what is the probability that exactly a fourth of the buyers would prefer red?
First, I think that .20 is taken from the total population and 1/4 of that is 5 or .05%?

2. Suppose that 50% of this population prefers the color red. If 14 buyers are randomly selected, what is the probability that less than 12 buyers would prefer red?
Is this one I have no clue at all.

3. Suppose that 30% of this population prefers the color green. If 16 buyers are randomly selected, what is the probability that between 2 and 5 (both inclusive) buyers would prefer green?
I have NO clue!!!

[BGM]

Hint: The number of n randomly selected buyers prefer red/green
~ Binomial(n, p), where p is the proportion of the population prefer red/green
http://en.wikipedia.org/wiki/Binomial_distribution

[Riverdale27]

Indeed the binomial distribution. It can give us the probability for k successes in n independent trials with a given probability for success p.

Answers:

a) 3,50%
b) 99,35%
c) 63,37%