Explanation Definition: If X is a random variable for the number of successes in n independent and identical repetitions of an experiment with success and failure as two possible outcomes and if p is a probability of success, then the probability for k success is defined as, P ( X = k ) = ( n k ) p k ( 1 − p ) n − k Here, k = 0 , 1 , ⋅ ⋅ ⋅ , n . Calculation: Consider a specific family with four children. The probability that the children will have brown eyes is 3 8 . The probability that at least two of the children have brown eyes is required. So, X ≥ 2 . This is a binomial distribution because there are fixed number of trials, that is, n = 4 . The trails are independent and the probability is the same for all trials. Define X as the number of children who have brown eyes. So, n = 4 , X ≥ 2 , p = 3 8 . The required probability can be written as, P ( X ≥ 2 ) = 1 − P ( X < 2 ) = 1 − { P ( X = 0 ) + P ( X = 1 ) } Use the probability formula and substitute these values to calculate the required probability. P ( X ≥ 2 ) = 1 − { ( 4 0 ) ( 3 8 ) 0 ( 1 − 3 8 ) 4 − 0 + ( 4 1 ) ( 3 8 ) 1 ( 1 − 3 8 ) 4 − 1 } Use the combination formula (

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

13th Edition

ISBN: 9781337605076

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 13.6, Problem 40PS

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The probability that at least two children have brown eyes if there are four children in specific family and the probability of a child having brown eyes is 38.

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Chapter 13.6, Problem 39PS

Chapter 13.6, Problem 41PS

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Chapter 13 Solutions

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

Ch. 13.1 - IN YOUR OWN WORDS What is the difference between...Ch. 13.1 - IN YOUR OWN WORDS Define probabilities?Ch. 13.1 - Prob. 3PS Ch. 13.1 - Prob. 4PS Ch. 13.1 - Prob. 5PS Ch. 13.1 - Prob. 6PS Ch. 13.1 - Prob. 7PS Ch. 13.1 - Prob. 8PS Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...

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The probability that at least two children have brown eyes if there are four children in specific family and the probability of a child having brown eyes is 3 8 .

Solution Summary: The author calculates the probability that at least two children will have brown eyes if there are four children in a specific family.

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The probability that at least two children have brown eyes if there are four children in specific family and the probability of a child having brown eyes is 38.

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The probability that at least two children have brown eyes if there are four children in specific family and the probability of a child having brown eyes is 3 8 .

Solution Summary: The author calculates the probability that at least two children will have brown eyes if there are four children in a specific family.

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To find: The probability that at least two children have brown eyes if there are four children in specific family and the probability of a child having brown eyes is 38.

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Chapter 13 Solutions

To find:

The probability that at least two children have brown eyes if there are four children in specific family and the probability of a child having brown eyes is 38.