A box contains 6 red balls, 4 blue balls, and 2 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
Show the answer and explanation
Correct answer
C. 5/22
Principle or equation
For drawing without replacement, the probability of two red balls is (number of red / total) * (number of red - 1) / (total - 1).
Why this answer is correct
Total balls = 6 + 4 + 2 = 12. Probability first red = 6/12 = 1/2. After one red is removed, there are 5 red left and 11 total. Probability second red = 5/11. Multiply: (1/2)*(5/11) = 5/22.
Example
If there are 3 red and 2 blue, probability of two red without replacement is (3/5)*(2/4)=3/10.
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