Question

Maddy has a bag of 36 marbles. The probability of picking green is 1 in 2, the probability of picking red is 1 in 3, and the probability of picking blue is 1 in 9. The only other color in the bag is black. Find the probability of Maddy picking a black marble.

Answer 1

Answer: 1 in 18

This is the same as writing the fraction 1/18

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Step-by-step explanation:

Since she has 36 marbles total, and the probability of picking green is 1 in 2, this means (1/2)*36 = 18 marbles are green.

Then she also has (1/3)*36 = 12 red marbles and (1/9)*36 = 4 blue marbles.

So far, that accounts for 18+12+4 = 34 marbles in all. That leaves 36-4 = 2 marbles left over that must be black, as it's the only color left.

From that, the probability of choosing a black marble is 2/36 = 1/18.

There's a 1 in 18 chance of Maddy picking a black marble.

1/18 = 0.0556 = 5.56% approximately