Assume we have a bag containing 4 red marbles and 6 green ma

Assume we have a bag containing 4 red marbles and 6 green marbles. A person randomly selected one marble and then without replacement of the first marble randomly selected a second marble. The probability of selecting 2 red marbles is:

a. Assume we have a bag containing 4 red marbles and 6 green marbles. A person randomly selected one marble and then without replacement of the first marble randomly selected a second marble. The probability of selecting 2 red marbles is:

b. Telephone calls at a police station follow a Poisson process and occur at an average rate of six calls per hour. The probability that there will be exactly four calls in an hour is:

c. Using the data from the question directly above, the probability that there will be at least four calls in an hour is:

d.  Assume there are 6 students in a seminar in Sociology. There is a unique project to be done by two students. The instructor has written down all possible pairs of students and will randomly select the pair. Student A and Student Z were wondering what were their chances of being selected. The probability of selecting this pair is

Solution

a. Probability of choosing 2 red marbles = Choosing 2 red from total 4 red / Choosing 2 marbles from 10 marbles

= 4C2 / 10C2 = 2/15 = 0.1333

b. P(X=x) = e^-6 * 6^x / x!

P(X=4) = e^-6 * 6⁴ / 4! = 0.1338

c. P(X >=4) = 1 - P(X<4) = 1 - P(X=0) - P(X=1)- P(X=2)- P(X=3)

= 1 - e^-6 * 6⁰ / 0! - e^-6 * 6¹ / 1! - e^-6 * 6² / 2! - e^-6 * 6³ / 3! = 0.8488

d. Number of ways of selecting A and Z as pair = 1

Total possible pairs = 6C2 = 15

Probability of choosing A and Z as pair = 1/15 = 0.0667