A bag of marbles contains 9 yellow marbles, 6 white marbles, 3 blue marbles, and 7 red marbles. A marble is picked at random and replaced. This is done a total of three times. What is the probability of picking a red marble, a white marble, and a blue marble?

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Quizplus · Accepted Answer

The total number of marbles is 9 + 6 + 3 + 7 = 25. The probability of picking a red marble is 7/25, a white marble is 6/25, and a blue marble is 3/25. Since the marble is replaced each time, the events are independent, and the probabilities can be multiplied together. Thus, the probability of picking a red, then a white, then a blue marble in any order is $(7/25) * (6/25) * (3/25) = 126/15,625$. However, since the order does not matter, we must account for all possible orders (RWB, WRB, BRW, RBW, WBR, BWR), which are 6. Multiplying the initial probability by the number of arrangements gives $126/15,625 * 6 = 126/15,625$, because the calculation already inherently accounts for all permutations of the sequence of picks.

A Bag of Marbles Contains 9 Yellow Marbles, 6 White 1625\frac { 1 } { 625 }6251​

A Bag of Marbles Contains 9 Yellow Marbles, 6 White $\frac { 1 } { 625 }$