Explanation Given: The probability of purchasing the book that people borrow is 40 % Number of people borrowing the book is 10 . Approach: The expanded expression of C ( n , x ) is given as; C ( n , x ) = n ! x ! ( n − x ) ! If p is the probability of success of an event and q is the probability of failure of an event. Then, the relationship between p and q is given as: q = 1 − p The probability of x successes in n independent trials is given by, P ( X = x ) C ( n , x ) p x q n − x Such that, x = 0 , 1 , 2 , 3 ......... , n Here, X is the binomial random variable and the probability distribution of X is called a binomial distribution. Calculation: Let X denote the number of people who purchase the book. Number of people borrowing the book is, n = 10 . The probability of people will purchase the book is, p = 40 % = 40 100 = 0.40 Calculate the value of q . Substitute 0.40 for q in the expression for q . p = 1 − 0.40 = 0.60 Write the expression to calculate the probability that at three will buy the book. P ( X ≥ 3 ) = 1 − P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) ( 1 ) Write the binomial distribution expression to calculate the probability of success of an event. P ( X = x ) = C ( n , x ) p x q n − x = n ! x ! ( n − x ) ! p x q n − x ( 2 ) Calculate the value of P ( X = 0 ) . Substitute 10 for n , 0 for x , 0.40 for p and 0.6 for q in equation ( 2 ) . P ( X = 0 ) = 10 ! 0 ! ( 10 − 0 ) ! ( 0

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Author: Tan

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Chapter 8.4, Problem 30E

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The probability that at least three will purchase the book.

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Chapter 8.4, Problem 29E

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Chapter 8 Solutions

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Ch. 8.1 - What is a random variable? Give an example.Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Three balls are selected at random without...Ch. 8.1 - 2.A coin is tossed four times. Let the random...Ch. 8.1 - A die is rolled repeatedly until a 6 falls...Ch. 8.1 - Cards are selected one at a time without...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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The probability that at least three will purchase the book.

Solution Summary: The author explains that the probability that at least three will purchase the book is 0.83.

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