A box contains 3 red balls, 5 blue balls, and 2 green balls. Two balls are drawn at random without replacement. What is the probability that the two balls are of different colors?
Show the answer and explanation
Correct answer
A. 31/45
Principle or equation
For drawing without replacement, the probability of an event is the number of favorable outcomes divided by the total number of outcomes. Use combinations or sequential probabilities.
Why this answer is correct
Total balls = 3+5+2=10. Total ways to draw 2 balls: C(10,2)=45. Favorable outcomes: two balls of different colors. Count the complement: both same color. Ways to choose 2 red: C(3,2)=3; 2 blue: C(5,2)=10; 2 green: C(2,2)=1. Total same color = 14. So different colors = 45 - 14 = 31. Probability = 31/45.
Example
If a box has 2 red and 3 blue, probability of drawing two different colors without replacement: total C(5,2)=10; same color: C(2,2)+C(3,2)=1+3=4; different=6; probability=6/10=3/5.
This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.