Question

A bag contains 8 red, 4 blue, and 4 yellow marbles.

What is the probability of randomly choosing 2 blue marbles without replacement?
Round to the nearest hundredth if needed.

Answer 1

Answer: 0.05

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Step-by-step explanation:

There are 4 blue out of 8+4+4 = 16 marbles total

The probability of picking blue the first time is 4/16 = 1/4. Let A = 1/4.

After we pick a blue marble, we have 4-1 = 3 left over out of 16-1 = 15 left over. The values go down by 1 because of the "without replacement" key phrase. The probability of picking blue again is 3/15 = 1/5. Let B = 1/5

Multiply the two values for A and B
A*B = (1/4)*(1/5) = 1/20

Convert to decimal form (use a calculator)
1/20 = 0.05

Alternatively, you can convert 1/4 and 1/5 to decimals first
A = 1/4 = 0.25
B = 1/5 = 0.20
and then multiply
A*B = 0.25*0.20 = 0.05

Note: the answer 0.05 is equivalent to 5%. You would move the decimal point 2 spots to the right to convert to a percentage.