Explanation Given: Two cards are drawn at random from an ordinary deck of 52 cards. Explanation: Consider the experiment of drawing 2 cards from an ordinary deck of 52 cards. Assume that, E represents the event that 2 cards of the same suit are drawn. The number of elements in the sample space will be equal to the number of ways of drawing 2-cards hand from an ordinary deck of 52 cards. That is, n ( S ) = C ( 52 , 2 ) = 52 ! 2 ! × ( 52 − 2 ) ! = 52 × 51 × 50 ! 2 × 1 × 50 ! = 1 , 326 There are 4 suits in an ordinary deck of 52 cards, spades, hearts, diamonds and clubs. Each suit has 13 cards. So, the number of elements in the event E will be equal to the number of ways of drawing 2 spades from 13 spades plus the number of ways of drawing 2 hearts from 13 hearts plus the number of ways of drawing 2 diamonds from 13 diamonds plus the number of ways of drawing 2 clubs from 13 clubs. That is, n ( E ) = C ( 13 , 2 ) + C ( 13 , 2 ) + C ( 13 , 2 ) + C ( 13 , 2 )

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.3, Problem 15E

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The probability that 2 cards of the same suit are drawn when 2 cards are drawn from an ordinary deck of 52 cards.

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The probability that 2 cards of the same suit are drawn when 2 cards are drawn from an ordinary deck of 52 cards.

Solution Summary: The author analyzes the probability of two cards of the same suit being drawn from an ordinary deck of 52 cards.

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