Selecting a Card A person selects a card from an ordinary

Chapter 5, Problem 20CQ

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QUESTION:

Selecting a Card A person selects a card from an ordinary deck of cards. If it is a black card, she wins $2. If it is a red card between or including 3 and 7, she wins $10. If it is a red face card, she wins $25; and if it is a black jack, she wins an extra $100. Find the expectation of the game.

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QUESTION:

Selecting a Card A person selects a card from an ordinary deck of cards. If it is a black card, she wins $2. If it is a red card between or including 3 and 7, she wins $10. If it is a red face card, she wins $25; and if it is a black jack, she wins an extra $100. Find the expectation of the game.

ANSWER:

Solution:

Step 1 of 2:

 Let us suppose that, a person selects a black card from a standard deck of cards is 26(13 spades + 13 clubs).

  That is,

                         P(black card) =

i). A person selects a red card between or including 3 or 7 is 10 (3,4,5,6,7 + 3,4,5,6,7).

    That is, 5 hearts + 5 diamonds = 10.  

    Thus,  

                 P(red card between 3 or 7) =

ii). A person selects a red face card is 6.

 That is, from diamond = king, queen, jack

               From heart = king, queen, jack.

  So, total faces = 3 + 3 = 6  

Then,

                      P(red face card) = 

iii). A person selects a black jack is 2.

That is, 1 from the spade and 1 from the club.

   Then,

               P(black jack) =


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