Stats 2
the weight of a t bone steak
Continous
List an example of two events that are dependent.
1.) Drawing one card from a standard deck, not replacing it, and then selecting another card
(a) List an example of two events that are independent.
1.) Rolling a die twice
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?
Add sum of trees =13 13!/ 5!*5!*3= 70072
What happens as the value of n increases and the probability of success remains the same? 4.2
As n increases, the distribution becomes more symmetric.
The probability that event A or event B will Occur :
P(a or b) = P(a)+P(b)-P(a and b)
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.
P(a)= 1/2= .5 P(b)=7/8=.875 .5*.875=.4375
correct graph of the probability distribution
Skews to the opposite side
three formulas that can be used to describe complementary events
*P(E)+P(E')=1 *P(E)equals=1minus−P(E') *P(E')equals=1minus−P(E)
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.
No, a carton can have a puncture and a smashed corner. Smashed corner and puncture: .04+.06 - .002 = .098
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.
P(a) 13/52 , P(b) 4/52 = .019
When an event is almost certain to happen, its complement will be an unusual event.
True, the complement would be an unusual event.
Is the number of points scored during a basketball game discrete or continuous?
Discrete
The annual traffic fatalities in a country
Discrete, because home attendance is a random variable that is countable (timeline graph)
The home attendance for football games at a University
Discrete, because home attendance is a random variable that is countable (timeline graph)
Explain how the complement can be used to find the probability of getting at least one item of a particular type.
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)
What are the two conditions that determine a probability distribution?
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.
Is the exact time it takes to evaluate 27+72 discrete or continuous?
The random variable is continuous
guessing the las digit of the price of the tv
The sample space is {0,1,2,3,4,5,6,7,8,9}. 10 total
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)?
10!/(10-3)!3!
Determine which numbers could not be used to represent the probability of an event.
*64/25, because probability values cannot be greater than 1. * −1.5, because probability values cannot be less than 0.
A probability experiment consists of rolling a fair 8-sided die. Find the probability of the event below. rolling a number greater than 7
1 divided by 8 = .125
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?
4*13*3 =156
Assuming that no questions are left unanswered, in how many ways can a six-question quiz with 4 multiple choice questions quiz be answered?
4*4*4*4*4*4=4096 (multiply by 6 questions)
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?
9*10*10*10*5=45000
What is a discrete probability distribution?
A discrete probability distribution lists each possible value a random variable can assume, together with its probability
If two events are independent, P(A|B)equals=P(B).
False; if events A and B are independent, then P(A and B)equals=P(A)times•P(B).
A probability experiment consists of rolling a fair 8-sided die. Find the probability of the event below. rolling a number greater than 77
1/8=.125
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?
.82 prob
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).
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 ????????
A standard deck of cards contains 52 cards. One card is selected from the deck.
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
Time required to download a file
Continuous
In a binomial experiement, what does it mean to say that each trial is independent of the other trials? 4.2
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
You toss a coin and roll a die. The event "tossing tails and rolling a 22 or 55" is a simple event.
False, the event is not simple because it consists of two possible outcomes
In most applications, discrete random variables represent counted data, while continuous random variables represent measured data.
True
The mean of a random variable represents the "theoretical average" of a probability experiment and sometimes is not a possible outcome.
True
What is the significance of the mean of a probability distribution?
It is the expected value of a discrete random variable
The number of different ordered arrangements of n distinct objects is n!.
True
When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? 4.1
The number of ordered arrangements of n objects taken r at a time.
A combination is an ordered arrangement of objects.
The statement is false. A true statement would be "A permutation is an ordered arrangement of objects."
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
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."
If two events are mutually exclusive, they have no outcomes in common.
True
When you calculate the number of combinations of r objects taken from a group of n objects what are you counting? Give an example.
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.