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Chapter 14 worksheet

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We are rolling two four- sided dice having the numbers 1, 2, 3, and 4 on their faces. Outcomes in the sample space are pairs such as (1,3) and (4,4)

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**A) How many elements are in the sample space?**

B) What is the probability that the total showing is even? C) What is the probability that the total showing is greater than six?

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Solutions A) 16 B) .5 C) 3/16

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An experimenter testing for extrasensory perception has five cards with pictures of a (s)tar, a (c)ircle, (w)iggly lines, a (d)ollar sign, and a (h)eart. She selects two cards without replacement. Outcomes in the sample space are represented by pairs such as (s,d) and (h,c).

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**A) How many elements are in this sample space?**

B) What is the probability that a star appears on one of the cards? C) What is the probability that a heart does not appear?

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solutions A) 20 B) 2/5 C) 3/5

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**For the next problems; a) Find the probability of the given event.**

b) Find the odds against the given event.

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Formula

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**Probability formula for computing odds**

If E’ is the complement of the event E, then the odds against E are

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**A total of three shows when we roll two fair dice.**

Questions A total of three shows when we roll two fair dice.

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Solutions a) b) First find P(E’) Then find

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**We draw a face card when we select 1 card randomly from a standard 52-card deck.**

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2) a) b) 10 to 3

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**Assume that we are drawing a 5-card hand from a standard 52-card deck.**

What is the probability that all cards are face cards? We have to remember the counting technique C(52,5) ways to select a 5-card hand from a 52-card deck.

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Combination Def. If we choose r objects from a set of n objects, we say that we are forming a combination of n objects taken r at a time. Notation C(n,r) = P(n,r) / r! = n! / [r!(n-r)!]

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**What is the probability that all cards are red?**

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0.025

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In a given year, 2,048,861 males and 1,951,379 females were born in the United States. If a child is selected randomly from this group, what is the probability that it is a female.

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**Do you remember how to solve this problem?**

Solution Do you remember how to solve this problem?

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**You are playing a game in which a single die is rolled**

You are playing a game in which a single die is rolled. Calculate the expected value for each game. Is the game fair? See next slide for question.

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If an odd number shows up, you win the number of dollars showing on the die. If an even number comes up, you lose the number of dollars showing on the die.

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The game is not fair.

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**You are playing a game in which a single die is rolled**

You are playing a game in which a single die is rolled. If a four or five comes up, you win $2; otherwise, you lose $1. 0, the game is fair.

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For the following problem, first calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.

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**Five hundred chances are sold at $5 apiece for a raffle**

Five hundred chances are sold at $5 apiece for a raffle. There is a grand prize of $500, two second prizes of $250, and five third prize of $100.

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**Now calculate the expected value.**

$3 to make the game fair.

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