Stats 2 – Flashcards
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Determine which numbers could not be used to represent the probability of an event.
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*64/25?, because probability values cannot be greater than 1.
* ??1.5, because probability values cannot be less than 0.
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three formulas that can be used to describe complementary events
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*?P(E)+?P(E')=1
*P(E)equals=1minus??P(E')
*?P(E')equals=1minus??P(E)
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You toss a coin and roll a die. The event? "tossing tails and rolling a 22 or 55?" is a simple event.
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False, the event is not simple because it consists of two possible outcomes
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You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is greater than 0.5
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The statement is false. The correct statement is? "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is exactly? 0.5."
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When an event is almost certain to? happen, its complement will be an unusual event.
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True, the complement would be an unusual event.
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Nine of the 50 digital video recorders? (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not? defective?
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.82 prob
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guessing the las digit of the price of the tv
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The sample space is {0,1,2,3,4,5,6,7,8,9}.
10 total
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A restaurant offers a? $12 dinner special that has 44 choices for an? appetizer, 1313 choices for an? entrée, and 33 choices for a dessert. How many different meals are available when you select an? appetizer, an? entrée, and a? dessert?
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4*13*3 =156
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The access code for a? car's security system consists of five digits. The first digit cannot be 33 and the last digit must be even. How many different codes are? available?
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9*10*10*10*5=45000
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Assuming that no questions are left? unanswered, in how many ways can a six?-question quiz with 4 multiple choice questions quiz be? answered?
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4*4*4*4*4*4=4096 (multiply by 6 questions)
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A probability experiment consists of rolling a fair 8?-sided die. Find the probability of the event below.
rolling a number greater than 7
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1 divided by 8 = .125
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A probability experiment consists of rolling a fair 8?-sided die. Find the probability of the event below.
rolling a number greater than 77
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1/8=.125
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?(a) List an example of two events that are independent.
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1.) Rolling a die twice
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List an example of two events that are dependent.
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1.) Drawing one card from a standard? deck, not replacing? it, and then selecting another card
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Explain how the complement can be used to find the probability of getting at least one item of a particular type.
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The complement of? "at least? one" is? "none." So, the probability of getting at least one item is equal to 1??P(none of the? items)
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If two events are? independent, ?P(A|B)equals=?P(B).
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False; if events A and B are? independent, then? P(A and ?B)equals=?P(A)times•?P(B).
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Two cards are selected from a standard deck of 52 playing cards. The first is replaced before the second card is selected. Find the probability of selecting a spade and then selecting a jack.
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P(a) 13/52 , P(b) 4/52 = .019
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A coin is tossed and an eight?-sided die numbered 1 through 88 is rolled. Find the probability of tossing a tail and then rolling a number greater than 11.
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P(a)= 1/2= .5 P(b)=7/8=.875
.5*.875=.4375
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In a sample of 1000 U.S.? adults,206 dine out at a resaurant more than once per week. TwoTwo U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.? adults, complete parts? (a) through? (d).
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Both adults dine out more than once per week:
P(a) 206/1000 =.206 * P(b) 206/1000=.206 --->
.206*.206= .042
Niether adults dines out more than once a week:
1-.206 ????????
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If two events are mutually? exclusive, they have no outcomes in common.
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True
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The probability that event A or event B will Occur :
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P(a or b) = P(a)+P(b)-P(a and b)
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A company that makes cartons finds that the probability of producing a carton with a puncture is .04?, the probability that a carton has a smashed corner is .06?, and the probability that a carton has a puncture and has a smashed corner is .002. Answer parts? (a) and? (b) below.
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No, a carton can have a puncture and a smashed corner.
Smashed corner and puncture:
.04+.06 - .002 = .098
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A standard deck of cards contains 52 cards. One card is selected from the deck.
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Club or diamond: 13/52=1/4 & 13/52=1/4
(1/4 +1/4=1/2)
club diamond heart: Same thing as above =3/4
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When you calculate the number of permutations of n distinct objects taken r at a? time, what are you? counting? 4.1
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The number of ordered arrangements of n objects taken r at a time.
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When you calculate the number of combinations of r objects taken from a group of n objects what are you? counting? Give an example.
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You are counting the number of ways to select r of the n objects without regard to order. An example of a combination is the number of ways a group of teams can be selected for a tournament.
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A combination is an ordered arrangement of objects.
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The statement is false. A true statement would be? "A permutation is an ordered arrangement of? objects."
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The number of different ordered arrangements of n distinct objects is? n!.
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True
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A? golf-course architect has five linden? trees,five white birch? trees, and three bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a? row, assuming that the trees are evenly? spaced?
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Add sum of trees =13
13!/ 5!*5!*3= 70072
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A horse race has 1010 entries and one person owns 33 of those horses. Assuming that there are no? ties, what is the probability that those three horses finish first comma second and, second and third ?(regardless of? order)?
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10!/(10-3)!3!
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What is a discrete probability? distribution?
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A discrete probability distribution lists each possible value a random variable can? assume, together with its probability
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What are the two conditions that determine a probability? distribution?
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The probability of each value of the discrete random variable is between 0 and? 1, inclusive, and the sum of all the probabilities is 1.
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What is the significance of the mean of a probability? distribution?
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It is the expected value of a discrete random variable
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In most? applications, discrete random variables represent counted? data, while continuous random variables represent measured data.
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True
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The mean of a random variable represents the? "theoretical average" of a probability experiment and sometimes is not a possible outcome.
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True
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The home attendance for football games at a University
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Discrete, because home attendance is a random variable that is countable (timeline graph)
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The annual traffic fatalities in a country
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Discrete, because home attendance is a random variable that is countable (timeline graph)
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Is the exact time it takes to evaluate 27+72 discrete or? continuous?
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The random variable is continuous
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Is the number of points scored during a basketball game discrete or? continuous?
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Discrete
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the weight of a t bone steak
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Continous
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Time required to download a file
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Continuous
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correct graph of the probability distribution
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Skews to the opposite side
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In a binomial? experiement, what does it mean to say that each trial is independent of the other? trials? 4.2
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Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials
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What happens as the value of n increases and the probability of success remains the? same? 4.2
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As n? increases, the distribution becomes more symmetric.
