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The founders of an online dating website believe there is a 61%61\% chance that a user believes in love at first sight. If 55 of the website's users are randomly selected to participate in a speed dating event, what is the probability that exactly 55 of them believe in love at first sight? Write your answer as a decimal rounded to the nearest thousandth.____

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Find probabilities using the binomial distributionright chevron icon

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Q. The founders of an online dating website believe there is a 61%61\% chance that a user believes in love at first sight. If 55 of the website's users are randomly selected to participate in a speed dating event, what is the probability that exactly 55 of them believe in love at first sight? Write 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=5n = 5, k=5k = 5, and p=0.61p = 0.61.
  2. Calculate C(5,5)C(5, 5): Calculate C(5,5)C(5, 5) which is 5!5!(5−5)!\frac{5!}{5!(5 - 5)!}. Since 0!0! is 11, C(5,5)C(5, 5) is 11.
  3. Solve (0.61)5(0.61)^5: Now, solve (0.61)5(0.61)^5. That's 0.61×0.61×0.61×0.61×0.610.61 \times 0.61 \times 0.61 \times 0.61 \times 0.61.
  4. Solve (0.61)5(0.61)^5: Now, solve (0.61)5(0.61)^5. That's 0.61×0.61×0.61×0.61×0.610.61 \times 0.61 \times 0.61 \times 0.61 \times 0.61.The calculation gives (0.61)5=0.0851(0.61)^5 = 0.0851.

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