Question

1.A person buys a ticket for a draw that is comprised of five digits from 0 to 9 and four letters; one winning ticket is drawn. Assuming that all the tickets have been sold, determine the probability of a person winning the draw.

2.A survey group of 10 basketball players are chosen at random from thirty college athletes and fifteen professionals. Determine the probability that at least 5 of the athletes chosen are college athletes.

Answer 1

1:

Assuming digits and letters can be repeated. Since each digit can be selected in 10 ways and each letter can be selected in 26 ways so possible number of different tickets is

10 *10*10*10*10 * 26*26*26*26 = 45,697,600,000

Out of these possible tickets only one is winning ticket so

P(win) = 1 / 45697600000

2:

Let X is a random variable shows the number of college athletes selected in the sample. Here X has hyper-geometric distribution with following parameters :

Population size: N = 30+15 = 45

Sample size: n = 10

Number of college athletes in population: M = 30

The probability that at least 5 of the athletes chosen are college athletes is