problemset 1-4 solutions

problemset 1-4 solutions - Problem Set 1 Solutions Question...

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Problem Set 1 Solutions Question 3 a. b. c. d. e. f. g. Question 4 a. b.
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Question 5 a. Use a three-way venn diagram b. Question 6 A group of 100 people are asked about their vegetable preferences. 4 people like both broccoli and cauliflower, 80 people like broccoli but not cauliflower, and 15 people like neither broccoli nor cauliflower. How many people like . . . C B 4 80 1 15 There are 100 people, so the numbers in the Venn diagram should sum to 100. This means there is 1 person who likes cauliflower but not broccoli. (a) cauliflower? 1 + 4 = 5 people who like cauliflower.
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(b) broccoli? 80 + 4 = 84 people who like broccoli. (c) either broccoli or cauliflower? 1 + 4 + 80 = 85 people who like either broccoli or cauliflower. (d) cauliflower but not broccoli? 1 person likes cauliflower but not broccoli. You had to figure this out to complete the Venn diagram. Question 7 Start with a standard deck of 52 cards and remove all the hearts and all the spades, leaving 13 red and 13 black cards. If you randomly select a card from this deck, find the probability that your card is . . . (a) an Ace. Let A be the event that you get an Ace. () 21 26 13 NA PA N == = Ω (b) not a face card. Let F be the event that you get a face card. () () ( ) 62 0 1 11 1 26 26 13 C NF PF N =− =− = = Ω 0 (c) neither red nor an Ace. Let R be the event that you get a red card. ( ) ( ) ( ) 13 2 1 14 12 6 26 26 26 26 26 13 CC PR A PR A PR PA PR A ∩= = + ⎡⎤ + − = ⎢⎥ ⎣⎦ (d) either black, even-numbered, or a Jack.
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Let B be the event that you get a black card, E be the event that you get an even card, and J be the event that you get a Jack. () ( ) ( ) ( ) ( ) ( )( ) ( ) 13 10 2 5 1 0 0 19 26 26 26 26 26 26 26 26 PB E J PB PE PJ PB E PB J PE J PB E J ∪= + + ∩− ∩+ =++−−−+= Question 8 Three of the main theme parks at Walt Disney World are Magic Kingdom, Epcot Center and MGM Studios. A travel website selects 50 of its customers and asks which of these three parks they have visited. The results for the 50 people are summarized below. 30 people have been to the Magic Kingdom 16 people have been to at least two of the parks 9 people have been to all three parks 18 people have been to Epcot Center 46 people have been to at least one of the parks 11 people have been to both Magic Kingdom and MGM Studios 11 people have been both Magic Kingdom and Epcot Center Use the above information to complete a three-way Venn diagram. MK MGM EC 4 3 9 2 9 2 17 4
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Problem Set 2 Solutions Question 1 There are 3 different numbers for the combination. So, we know that we have three choices. We will use the BCR for this problem, i.e. the total number of choices is equal to (# of choices for option 1) * (# of choices for option 2) * … In our case we only have 3 choices, the 3 numbers of the combination. a) We have no restrictions, so each option has 40 choices (0 thru 39 is 40 numbers). Therefore part a is 3 40 64000 = b) We have the restriction that no 2 consecutive numbers are the same. This restriction does not affect the 1 st number, so we have 40 choices for the 1 st number. Since the 2 nd number can’t be the same as the first number, we have only 39 choices for it. Since the 3
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This note was uploaded on 03/05/2009 for the course STAT 225 taught by Professor Martin during the Fall '08 term at Purdue.

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problemset 1-4 solutions - Problem Set 1 Solutions Question...

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