A box contains 6 red balls and 4 blue balls. Two balls are drawn at random without replacement. What is the probability that the two balls are of the same color?
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Correct answer
A. 7/15
Principle or equation
For drawing without replacement, the probability of an event is the number of favorable outcomes divided by the total number of equally likely outcomes. Use combinations: C(n,k) = n!/(k!(n-k)!).
Why this answer is correct
Total ways to draw 2 balls from 10: C(10,2)=45. Favorable: both red: C(6,2)=15; both blue: C(4,2)=6; total favorable=21. Probability=21/45=7/15.
Example
If there are 3 red and 2 blue, drawing two same color: C(3,2)+C(2,2)=3+1=4 over C(5,2)=10, so 2/5.
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