winniethepooh wrote:Mogo have nine cards out of which 2 are red, 3 are blue and 4 are green, what is the probability that he picks all 3 colors in three picks?
P(first marble is R) = 2/9. (9 marbles, 2 of which are red)
P(second marble is B) = 3/8. (8 marbles left, 3 of which are blue)
P(third marble is G) = 4/7. (7 marbles left, 4 of which are green).
Since we want all of the events above to happen together, we multiply the fractions:
P(RBG) = 2/9 * 3/8 * 4/7 = 1/21.
Since any arrangement of RGB will yield one of each color, we multiply the result above by the number of ways to arrange the 3 letters RBG.
Number of ways to arrange 3 elements = 3! = 6.
P(one of each color) = 6 * 1/21 = 2/7.
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