if two balls are drawn without replacement from a box containing 4 blue balls, 3 yellow balls, and 2 white balls, what is the probability of getting 2 yellow balls? (write your answer as a fraction in lowest terms.)
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To find the probability of drawing 2 yellow balls, we need to calculate the number of favorable outcomes (drawing 2 yellow balls) and divide it by the total number of possible outcomes.
First, let's determine the total number of balls in the box:
Total balls = (number of blue balls) + (number of yellow balls) + (number of white balls)
= 4 + 3 + 2
= 9
Next, we'll calculate the number of favorable outcomes, which is drawing 2 yellow balls. Since we need to draw without replacement, we'll consider it as two separate events.
For the first ball, the probability of drawing a yellow ball is:
Probability of drawing a yellow ball on the first draw = (number of yellow balls) / (total number of balls)
= 3 / 9
= 1 / 3
Now, after drawing the first yellow ball, we have 8 balls left, including 2 yellow balls. Therefore, the probability of drawing a second yellow ball is:
Probability of drawing a yellow ball on the second draw = (number of yellow balls - 1) / (total number of balls - 1)
= (2 - 1) / (8 - 1)
= 1 / 7
To find the overall probability of drawing 2 yellow balls, we multiply the probabilities of both events since they are independent:
Overall probability = Probability of first event * Probability of second event
= (1/3) * (1/7)
= 1/21
Therefore, the probability of drawing 2 yellow balls is 1/21.