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C HAPTER 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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S OLUTIONS 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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F ORMULA

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P ROBABILITY FORMULA FOR COMPUTING ODDS If E’ is the complement of the event E, then the odds against E are

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

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S OLUTIONS 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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A SSUME 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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C OMBINATION 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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S OLUTION Do you remember how to solve this problem?

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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. 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. There is a grand prize of $500, two second prizes of $250, and five third prize of $100.

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N OW CALCULATE THE EXPECTED VALUE. $3 to make the game fair.

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