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Selecting a Card A person selects a card from an ordinary
Chapter 5, Problem 20CQ(choose chapter or problem)
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.
Questions & Answers
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) =