A bag contains 6 red balls and 4 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are the same color?
Show the answer and explanation
Correct answer
B. 7/15
Principle or equation
For drawing without replacement, use combinations. The probability of an event is the number of favorable outcomes divided by the total number of outcomes.
Why this answer is correct
Total ways to draw 2 balls from 10: C(10,2) = 45. Ways to draw 2 red: C(6,2) = 15. Ways to draw 2 blue: C(4,2) = 6. Total favorable = 21. Probability = 21/45 = 7/15.
Example
If there are 5 red and 3 blue, probability both same = (C(5,2)+C(3,2))/C(8,2) = (10+3)/28 = 13/28.
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