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Qurrent learning objective: Binomial Distribution Question 8 Score: 0 of 4 points The Jones family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child being a girl is 0.5 , find the probability that the Jones family had: The probability that the Jones family had at least 5 girls is Enter your answer b. at most 3 girls? The probability that the Jones family had at most 3 girls is Enter your answer

Ask by Norton Reid. in the United States
Mar 15,2025

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- The probability of having at least 5 girls is \( \frac{7}{64} \). - The probability of having at most 3 girls is \( \frac{21}{32} \).

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The binomial distribution can be a fun way to explore probabilities, especially with the classic scenario of having children. It tells us that when we assume the probability of having a girl or a boy is equal (0.5), we can use the formula for binomial probability: \( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \). For the Jones family's 6 children, you can calculate the probabilities for different values of \( k \) (number of girls), where \( n = 6 \) and \( p = 0.5 \). Now, for the at least 5 girls scenario, you’ll want to calculate \( P(X = 5) + P(X = 6) \). For at most 3 girls, it's the sum of probabilities for \( P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \). Enjoy crunching the numbers, and you might just find the answers to these charming family statistics!

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