Mario has 3 red marbles and 3 blue marbles in a box. He picks two marbles randomly without looking. What is the probability that both marbles are red?
Possible outcomes:
R1R2 B1B2 R1B1 B1R1
R1R3 B1B3 R1B2 B2R1
R2R1 B2B1 R1B3 B3R1
R2R3 B2B3 R2B1 B1R2
R3R1 B3B1 R2B2 B2R2
R3R2 B3B2 R2B3 B3R2
(6) (6) R3B1 B1R3
R3B2 B2R3
R3B3 B3R3
(9) (9)
Total of 30 possible events, but only 6 favorable events. Therefore, P(2 red marbles) = 6/30 = 1/5
Another way, using combinations:
C (3 , 2) / C (6, 2) = [ 3! / (2! * (3-2)! ] / [ 6! / (2! * (6-2)!) ] = 3 / 15 = 1/5
09/21/2021
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