A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. Two marbles are drawn at random without replacement. What is the probability that the first marble is red and the second marble is blue?
Show the answer and explanation
Correct answer
A. 1/11
Principle or equation
For dependent events without replacement, multiply the probability of the first event by the conditional probability of the second event given the first.
Why this answer is correct
Total marbles = 4+3+5 = 12. P(first red) = 4/12 = 1/3. After removing a red, there are 11 marbles left, 3 of which are blue. P(second blue | first red) = 3/11. Multiply: (1/3)*(3/11) = 3/33 = 1/11.
Example
If there were 2 red and 2 blue, P(red then blue) = (2/4)*(2/3) = 1/3.
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