Binomial
Layla has a coin that has a 60% chance of showing heads each time it is flipped. She is going to flip the coin 5 times. Let X represent the number of heads she gets.
What is the probability that she gets more than 3 heads?
0.34
As a part of a customer loyalty program, a restaurant's computer chooses orders at random to receive a free appetizer. Each order has a 1 in 18 chance of receiving a free appetizer.. (Each order is limited to one free appetizer.) Let X be the number of orders the restaurant fills in a day until they give away the first appetizer. Assume that each order getting the appetizer is independent.
Find the probability that the restaurant first gives away an appetizer on the 6th order of the day.
0.0414
Aja's favorite cereal is running a promotion that says 1-in-4 boxes of the cereal contain a prize. Suppose that Aja is going to buy 5 boxes of this cereal, and let X represent the number of prizes she wins in these boxes. Assume that these boxes represent a random sample, and assume that prizes are independent between boxes.
What is the probability that she wins at most 1 prize in the 5 boxes?
Binomial
Philip ran out of time while taking a multiple-choice test and plans to guess on the last 4 questions. Each question has 5 possible choices, one of which is correct. Let X= the number of answers Philip correctly guesses in the last 4 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
0.41
What are the Geometric Conditions?
1) 2 possible outcomes
2) P(success) is the same for each observation
3) all n observations are independent
4) variable of interest is the # of trials needed to obtain first success
Akhila works for a company with over 1000 employees, of whom 83% have pierced ears. Every year, each employee draws another employee's name and gives them a gift. Let T be the number of names Akhila draws until she draws an employee's name who does not have pierced ears.
Geometric
What are the 4 binomial Conditions?
1) 2 possible outcomes
2) P(success) is the same for each observation
3) all n observations are independent
4) n observations
Mr. Garcia notes that in 84% of the papers his former students have turned in, they cited their sources incorrectly. He plans to go through these papers at random to find one with incorrect citations for a lesson on citing with his current students. Assume that incorrect citations are independent between papers. Let N be the number of papers Mr. Garcia selects until he finds one with the sources cited incorrectly.
Find the probability that the 3rd paper Mr. Garcia selects will be the first with the sources cited incorrectly.
0.0215
Haylee selects 1010 small businesses at random from her state's directory. Let BB be the number of businesses she selects that have websites.
Binomial