Problem

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability that both marbles are white
A. $\frac{3}{8}$
B. $\frac{3}{32}$
c. $\frac{9}{56}$
D. $\frac{3}{28}$

Answer

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Answer

Final Answer: The probability that both marbles are white is \(\boxed{\frac{3}{28}}\).

Steps

Step 1 :The problem is asking for the probability of drawing two white marbles without replacement from a box containing 3 white, 2 green, 2 red, and 1 blue marble.

Step 2 :This is a combination problem, and the probability can be calculated by dividing the number of successful outcomes by the total number of outcomes.

Step 3 :The successful outcomes are the ways to choose 2 white marbles from 3, and the total outcomes are the ways to choose 2 marbles from 8 (3 white, 2 green, 2 red, and 1 blue).

Step 4 :The number of successful outcomes is 3.

Step 5 :The total number of outcomes is 28.

Step 6 :The probability is calculated as \(\frac{3}{28}\).

Step 7 :Final Answer: The probability that both marbles are white is \(\boxed{\frac{3}{28}}\).

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