Q.29 A deck of cards contains 52聽car... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 6: Q.29 (page 356)

A deck of cards contains $52$ cards, of which $4$ are aces. You are offered the following wager: Draw one card at random from the deck. You win $$10$ if the card drawn is an ace. Otherwise, you lose $$ 1$ . If you make this wager very many times, what will be the mean amount you win?
(a) About 鈭� $$1$ , because you will lose most of the time.
(b) About $$ 9$ , because you win $$10$ but lose only $$ 1$ .
(c) About 鈭� $$0.15$ ; that is, on average you lose about $15$ cents. (d) About $$ 0.77$ ; that is, on average you win about $77$ cents.
(e) About $$ 0$ , because the random draw gives you a fair bet.

Short Answer

Expert verified

The correct option is (C) About $- $ 0.15$ ; that is, on average you lose about $15$ cents.

Step by step solution

Given Information

Given in the question that a deck of cards contains $52$ cards, of which $4$ are aces. You are offered the following wager: Draw one card at random from the deck. You win $$ 10$ if the card drawn is an ace. Otherwise, you lose $$ 1$ .

Explanation

A deck of cards contains $4$ aces out of $52$ cards.

The number of positive outcomes divided by the total number of possible outcomes equals the probability:

localid="1649915202706" $P (win) = \frac{# of favorable outcomes}{# of possible outcomes} = \frac{4}{52} = \frac{1}{13}$

localid="1649915218751" $P (loss) = \frac{# of favorable outcomes}{# of possible outcomes} = \frac{48}{52} = \frac{12}{13}$
The expected value is the sum of the product of each possibility with its probability: