Question

An urn contains 15 different colored marbles, 7 are red, 5 are blue, and 3 are green. Part 1. If two balls are randomly picked from the urn without replacement a) b) Determine the sample space What is the probability of grabbing a red marble on the first pick and then a green marble on the second pick? Did you use the classical or empirical approach to calculate the probability in part b? Are these events independent or dependent? Disjoint or not disjoint? c) d) Part 2. If two balls are randomly picked from the urn with replacement... Determine the sample space What is the probability of grabbing a blue marble on the first pick and then a green marble on the second pick? Did you use the classical or empirical approach to calculate the probability in pa Are these events independent or dependent? Disjoint or not disjoint? a) b) rt b? c) d) Part 3. What is the probability of choosing a red marble or a blue marble?

Answer 1

Part 1:

a) The sample space here contain the possible combinations of the 2 balls taken out:

{RR, BB, GG, RG, RB, BG}

b) Probability of getting red marble first and then a green marble is computed here as:

= (7/15)*(3/14) = 0.1

Therefore 0.1 is the required probability here.

c) Empirical probability is computed by experimenting in reality but theoritically calculated probability is called classical probability. As we did not really experiment to find the required probability, therefore classical probability is the correct answer here

d) The events are dependent, because the probability of drawing a particular colour ball on the second draw depends on the colour of ball drawn on the first draw. For example if the first ball drawn is red, the probability of drawing a red ball on second draw would be less than when the first ball drawn was a non red ball.