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A psychology professor surveyed her class and determined that 59%59\% of the students have acrophobia, a fear of heights. If 22 of the students are chosen at random, what is the probability that 00 have acrophobia?\newlineWrite your answer as a decimal rounded to the nearest thousandth.____

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Q. A psychology professor surveyed her class and determined that 59%59\% of the students have acrophobia, a fear of heights. If 22 of the students are chosen at random, what is the probability that 00 have acrophobia?\newlineWrite your answer as a decimal rounded to the nearest thousandth.____
  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=2n = 2, k=0k = 0, and p=0.59p = 0.59.
  2. Calculate Combination: Calculate C(2,0)C(2, 0) which is 2!0!(2−0)!\frac{2!}{0! (2 - 0)!}.C(2,0)=1C(2, 0) = 1.
  3. Solve (0.59)0(0.59)^0: Solve (0.59)0(0.59)^0 which is 11 because any number to the power of 00 is 11.
  4. Simplify (1−0.59)(2−0)(1 - 0.59)^{(2 - 0)}: Simplify (1−0.59)(2−0)(1 - 0.59)^{(2 - 0)} which is (0.41)2(0.41)^2.
  5. Calculate (0.41)2(0.41)^2: Calculate (0.41)2(0.41)^2.(0.41)2=0.1681(0.41)^2 = 0.1681.
  6. Multiply Values Together: Multiply all the values together: P(X=0)=1×1×0.1681P(X = 0) = 1 \times 1 \times 0.1681.\newlineP(X=0)=0.1681P(X = 0) = 0.1681.
  7. Round to Nearest Thousandth: Round the answer to the nearest thousandth.\newlineP(X=0)=0.168P(X = 0) = 0.168.

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