At a certain college, 16% of the calculus students get As,

Light bulbs manufactured by a certain factory last a random time between 400 and 1200 hours. What is the probability that, of eight such bulbs, three burn out before 550 hours, two burn out after 800 hours, and three burn out after 550 but before 800 hours?

An urn contains 100 chips of which 20 are blue, 30 are red, and 50 are green. We draw 20 chips at random and with replacement. Let B, R, and G be the number of blue, red, and green chips, respectively. Calculate the joint probability mass function of B, R, and G.

Suppose that each day the price of a stock moves up 1/8 of a point with probability 1/4, remains the same with probability 1/3, and moves down 1/8 of a point with probability 5/12. If the price fluctuations from one day to another are independent, what is the probability that after six days the stock has its original price?

At a certain college, 16% of the calculus students get As, 34% Bs, 34% Cs, 14% Ds, and 2% Fs. What is the probability that, of 15 calculus students selected at random, five get Bs, five Cs, two Ds, and at least two As?

Suppose that 50% of the watermelons grown on a farm are classified as large, 30% as medium, and 20% as small. Joanna buys five watermelons at random from this farm. What is the probability that (a) at least two of them are large; (b) two of them are large, two are medium, and one is small; (c) exactly two of them are medium if it is given that at least two of them are large?

Suppose that the ages of 30% of the teachers of a country are over 50, 20% are between 40 and 50, and 50% are below 40. In a random committee of 10 teachers from this country, two are above 50. What is the probability mass function of those who are below 40?

(Genetics) As we know, in humans, for blood type, there are three alleles A, B, and O. The alleles A and B are codominant to each other and dominant to O. A man of genotype AB marries a woman of genotype BO. If they have six children, what is the probability that three will have type B blood, two will have type A blood, and one will have type AB blood?

(Genetics) Let p and q be positive numbers with p + q = 1. For a gene with dominant allele A and recessive allele a, let p2, 2pq, and q2 be the probabilities that a randomly selected person from a population has genotype AA, Aa, and aa, respectively. A group of six members of the population is selected randomly. Determine the value of p that maximizes the probability of the event of obtaining two AAs, two Aas, and two aas.

Customers enter a department store at the rate of three per minute, in accordance with a Poisson process. If 30% of them buy nothing, 20% pay cash, 40% use charge cards, and 10% write personal checks, what is the probability that in five operating minutes of the store, five customers use charge cards, two write personal checks, and three pay cash?