an urn contains 6 blue, 2 yellow, and 2 gray marbles. two marbles are randomly drawn from the urn. find the…

an urn contains 6 blue, 2 yellow, and 2 gray marbles. two marbles are randomly drawn from the urn. find the probability the two marbles are the same color.\n\n$\frac{11}{25}$\n$\frac{22}{45}$\n$\frac{17}{45}$\n$\frac{17}{50}$

an urn contains 6 blue, 2 yellow, and 2 gray marbles. two marbles are randomly drawn from the urn. find the probability the two marbles are the same color.\n\n$\frac{11}{25}$\n$\frac{22}{45}$\n$\frac{17}{45}$\n$\frac{17}{50}$

Answer

Explanation:

Step1: Total marbles and combinations

Total marbles: (6 + 2 + 2 = 10). Total ways to draw 2: ( \binom{10}{2} = \frac{10 \times 9}{2} = 45 ).

Step2: Blue same color ways

Blue marbles: 6. Ways: ( \binom{6}{2} = \frac{6 \times 5}{2} = 15 ).

Step3: Yellow same color ways

Yellow marbles: 2. Ways: ( \binom{2}{2} = 1 ).

Step4: Gray same color ways

Gray marbles: 2. Ways: ( \binom{2}{2} = 1 ).

Step5: Favorable outcomes and probability

Favorable: (15 + 1 + 1 = 17). Probability: ( \frac{17}{45} ).

Answer:

C. ( \frac{17}{45} )