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Finn bought new equipment for his bowling alley, including a ball return machine. There is a 51%51\% chance that the machine returns a bowling ball with the finger holes facing up.\newlineIf the machine returns 33 bowling balls, what is the probability that exactly 11 ball will have the finger holes facing up?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline

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Q. Finn bought new equipment for his bowling alley, including a ball return machine. There is a 51%51\% chance that the machine returns a bowling ball with the finger holes facing up.\newlineIf the machine returns 33 bowling balls, what is the probability that exactly 11 ball will have the finger holes facing up?\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____\newline
  1. Use Binomial Probability Formula: Use the binomial probability formula: P(X=k)=C(n,k)⋅(p)k⋅(1−p)(n−k)P(X = k) = C(n, k) \cdot (p)^k \cdot (1-p)^{(n-k)}. Here, n=3n = 3, k=1k = 1, and p=0.51p = 0.51.
  2. Calculate C(3,1)C(3, 1): Calculate C(3,1)C(3, 1) which is 3!1!×(3−1)!=31×2=32=1.5\frac{3!}{1! \times (3 - 1)!} = \frac{3}{1 \times 2} = \frac{3}{2} = 1.5. This is incorrect because C(3,1)C(3, 1) should be an integer.

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