ALL of the following questions come from this problem: A Jar has 25 Red, 15 Blue

Question

ALL of the following questions come from this problem: A Jar has 25 Red, 15 Blue, and 10 Green marbles in it. (denoted events R,B,G) Calculate all to the following probabilities:


One marble drawn at random, probability it is green?
Probability a marble drawn at random is not blue.
THE REST OF THE PROBLEMS ARE FROM THE FOLLOWING SCENARIO:
drawing three marbles all at once.

What is the probability that all three are red?
Probability none are red?
Probability all 3 are green?
Probability at least one of the three is red?
Probability you get 2 red and 1 blue?
probability exactly 2 are red?
Probability you get 1 of each color?
Expected number of red mables?
Expected number of green marbles.

Explanation / Answer

No of green marbles = 10; No of marbles totally = 50; Hence prob. of random marble being green = 10/50 = 0.2 No of non blue marbles = 25 + 10 = 35; Hence prob. of random marble being not blue = 35/50 = 0.7 Three marbles drawn at once: P (None red) = 25/50 * 24/49 * 23/48 = 0.117 P (all green) = 10/50 * 9/49 * 8/48 = 0.006 P (at least 1 red) = P(1 red) + P (2 red) + P (3 red) = 25/50 * 25/49 * 24/48 + 25/50 * 24/49 * 25/48 + 25/50 * 24/49 * 23/48 = 0.372 P ( 2 red 1 blue) = 25/50*24/49*15/48 = 0.076 P (Exactly 2 red) = 25/50 * 24/49 * 25/48 = 0.128 P (1 of each colour) = 25/50 * 15/49 * 10/48 = 0.032 E (Red marbles) = 1*P(1 red) + 2*P(2 red) + 3*P(3red) = 1*(25/50) + 2*(25/50 * 24/49) + 3*(25/50 * 24/49 * 23/48) = 1.34 E (blue marbles) = 1*P(1 blue) + 2*P(2 blue) + 3*P(3 blue) = 1*(15/50) + 2*(15/50*14/49) + 3*(15/50*14/49*13/48) = 0.541

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