Explanation Given Information: Kent's tents has four red tents and three green tents in stock and four tents are selected at random by Karin. Formula Used: Step1: Determine total number of outcomes n ( S ) = C ( n , r ) . Step2: Determine the number of favorable outcomes n ( E ) = C ( n , r ) If the outcomes of an event are equally likely to occur, then the probability of an event E, is given by P ( E ) = n ( E ) n ( S ) Where n ( E ) is the number of favorable outcomes and n ( S ) is the total number of outcomes. The unordered set of r items chosen from n taken r at a time is given by rule of combination C ( n , r ) = n ! r ! ( n − r ) ! If there is a random variable X which has values x 1 , x 2 , ... , then the probability distribution of the event includes the probabilities such as X = x 1 , X = x 2 and the sum of these probabilities is always 1 . For the random variable X, P ( X = x ) represents the random variable X with the particular value of x. Calculation: Consider the total number of tents in stock four red tents and three green tents, n = 7 Evaluate the total number of outcomes n ( S ) by applying combinations C ( n , r ) = n ! r ! ( n − r ) ! where n = 7 and r = 4 . C ( 7 , 4 ) = 7 ! 4 ! ( 7 − 4 ) ! = 7 × 6 × 5 × 4 ! 4 ! ( 3 ) ! = 7 × 6 × 5 3 × 2 × 1 n ( S ) = 35 Since there are four red tents then the possible values of selecting red tent at random, variable X are x 1 = 1 , x 2 = 2 , x 3 = 3 , x 4 = 4 Evaluate the number of favorable outcomes n ( E ) by applying combinations C ( n , r ) = n ! r ! ( n − r ) ! If, x 1 = 1 Choose one red tent as, C ( 4 , 1 ) = 4 ! 1 ! ( 4 − 1 ) ! C ( 4 , 1 ) = 4 × 3 ! ( 3 ) ! C ( 4 , 1 ) = 4 Choose three green tent as, C ( 3 , 3 ) = 3 ! 3 ! ( 3 − 3 ) ! C ( 3 , 3 ) = 3 ! 3 ! × 0 C ( 3 , 3 ) = 1 Therefore, the total number of choices for choosing one red tent and three green tents is 4 × 1 = 4 . If, x 2 = 2 Choose two red tents as, C ( 4 , 2 ) = 4 ! 2 ! ( 4 − 2 ) ! C ( 4 , 2 ) = 4 × 3 × 2 ! 2 ! ( 2 × 1 ) C ( 4 , 2 ) = 6 Choose two green tents as, C ( 3 , 2 ) = 3 ! 2 ! ( 3 − 2 ) ! C ( 3 , 2 ) = 3 × 2 ! 2 ! × 1 C ( 3 , 2 ) = 3 Therefore, the total number of choices for choosing two red tent and two green tents is 6 × 3 = 18

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Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8.1, Problem 51E

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To calculate: The probability distribution and the value of P(X≥2) where X is a number of red tents when four tents are selected at random if Kent's tents has four red tents and three green tents in stock.

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Chapter 8.1, Problem 50E

Chapter 8.1, Problem 52E

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Chapter 8 Solutions

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The probability distribution and the value of P ( X ≥ 2 ) where X is a number of red tents when four tents are selected at random if Kent's tents has four red tents and three green tents in stock.

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To calculate: The probability distribution and the value of P(X≥2) where X is a number of red tents when four tents are selected at random if Kent's tents has four red tents and three green tents in stock.

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