In a bowl containing 10 marbles, 5 are blue and 5 are pink. If 2 marbles are picked randomly, what is the probability that the 2 marbles will not both be pink?
Show Hint
- \( \tfrac{2}{9} \)
- \( \tfrac{5}{6} \)
- \( \tfrac{7}{9} \)
- \( \tfrac{7}{8} \)
The Correct Option is C
Solution and Explanation
\[ \binom{10}{2} = 45 \]
Step 2: Ways to pick 2 pink marbles.
\[ \binom{5}{2} = 10 \]
Step 3: Probability of both pink.
\[ \frac{10}{45} = \frac{2}{9} \]
Step 4: Probability of not both pink.
\[ 1 - \frac{2}{9} = \frac{7}{9} \]
Final Answer: \[ \boxed{\tfrac{7}{9}} \]
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