NAMES________________________PROJECT V DUE MAR. 24, 2005 SHOW ALL YOUR WORK. PUT EACH PROBLEM ON A SEPARATE SHEET OF PAPER. USE THIS PAGE AS YOUR COVER SHEET. MAXIMUM NUMBER PER GROUP IS THREE.1. An experiment consists of tossing a fair coin, and a six-sided die. A. Find the sample space of this experiment.B. Find the probability of getting heads and an even number.C. Find the probability of getting heads and a number greater than 4.D. Find the probability of getting tails and an odd number.2. A ball is drawn randomly from a jar that contains five red balls, two white balls, and one yellow ball. Find the probability of the following events:A. A red ball is drawn.B. The ball drawn is not yellow.C. A purple ball is drawn.D. Neither a white nor a yellow ball is drawn.E. The ball drawn is not whiteF. A red, white or yellow ball is drawn.3. A poker hand, consisting of 5 cards, is dealt from a standard deck of 52 cards. Find the probability that the hand contains the cards described.A. Five hearts (flush)B. Five face cardsC. Royal flush (A, K, Q, J, 10 of same suit)D. A hand with three 8s and two Js (full house)4. An American roulette wheel has 38 slots: numbers 1 – 36 and 0, 00.A. Find the probability that the ball lands in an odd numbered slot.B. Find the probability that the ball lands in slot with a number greater than 31.C. Find the probability that the ball lands in an odd numbered slot or in a slot with number greater than 31.5. A bag contains two silver dollars and eight slugs(worthless). You pay 50cents for the privilege to reach into the bag an take a coin which you getto keep. What is the expected value of this game?6. A sweepstakes offers a first prize of $1 million, second prize of $100,000 and a third prize of $10,000. Suppose that 2 million people enter the contest and three names are drawn randomly of the 3 prizes.A. Find the Expected winnings for a person participating in the contest.B. Is it worth paying a $1 to enter the sweepstakes?7. A game consists of drawing a card from a 52 card standard deck. You win $13 if you draw an ace. What is a “fair price” to pay to play this game?8. A card is drawn at random from a standard 52 card deck. Determine whether the events E and F are mutually exclusive, the find the probability of FE .A. Event E: The card is a face card. Event F: The card is a spade.B. Event E: The card is a heart. Event F: The card is a spade.C. Event E: The card is a club. Event F: The card is a kingD. Event E: The card is a 5. Event F: The card is a 2.9. Among a certain group of friends, watching football and playing triviaare two of their favorite pastimes. 27% of the time, they go to the Ft.Lowell Depot to watch football, while 57% of the time they win attrivia. 68.6% of the time they go to either the Ft. Lowell Depot or win attrivia. Are these events independent? Show why or why not.10. In a survey, 750 people were asked “Is ACTIVISION ANTHOLOGY” (PS-2 game with all of Activision’s Atari 2600 titles) the best computer game ever? The results were formatted in the table below:Yes(Y)No(N)Don’t Know(K)TotalM 230 54 97 381W 68 124 177 369Total298 178 274 750Compute the following:A. P(M|N)B. P(W|Y)C. P(Y|M)D.
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