Binomial Random Variables
For X to be a binomial random variable, there must be a finite number of trials, the probability of "success" must be the same for each trial, the trials must be independent of each other... I feel like I'm missing something!
What is there are two outcomes for each trial?
The formula used for conditional probability
What is (P(A and B))/(P(B))?
Expected value is a fancy way of saying this, something I hope you never call me
What is the mean?
What is joint frequency?
Hey Siri, flip a coin! Flip it again! Again!! I flip a coin 13 times and count the number of tails. Have I a binomial random variable?
What is YES!
Ben and Jerry took notice of what their customers were ordering at their ice cream stand and noted the following:
P(Brownie Batter) = 0.4
P(Cherry Garcia) = 0.2
P(Chunky Monkey) = 0.4
P(Brownie Batter and Cherry Garcia) = 0.17
Given that a customer ordered Cherry Garcia, what is the probability that they also ordered Brownie Batter?
What is 0.85?
When X = -6, P(X) = 0.25. When X = 3, P(X) = 0.5. When x = 6, P(X) = 0.25. What is the E[X]?
You draw a card at random from a deck that has 3 black cards and 7 red cards. What is the probability of not drawing a black card?
What is 0.7?
Laney Industries produces WindBuds, the best alternative to AirPods--only 3% of our WindBuds are defective! Quality control randomly selected 12 pairs of WindBuds from the assembly line to test. Binomial RV?
What is YES!
Whataburger noted what type of food it sold this past week. Here are the results:
30% of people ordered a hamburger
10% ordered fries
6% ordered both a burger and fries
Given that a person ordered a burger, what is the probability that they also ordered fries?
What is 0.2?
Heather owns and operates Haskell Coffee Shop. The city of Auburn, AL, where her coffee shop is located, recently enacted a ban of all foam cups to help protect the environment. Instead of switching to paper cups, Heather has decided to take the risk of being fined by the city. She anticipates that this will save her $20,000! She estimates that there is a 13% chance the city finds out and fines her $165,000. What is her estimated value of continuing to use foam cups?
What is -$4,050?
There are 6 blue marbles, 3 red marbles, and 5 yellow marbles in a bag. What is the probability of drawing a blue or red marble on the first draw?
What is 9/14?
Auburn University wants to know if their students enjoy their experience during their 4 (or maybe more) years here. Is this a binomial RV?
What is NO!
30% of all car sales this past year were SUVs and 15% of the SUVs sold were white. 15% of sales were trucks; 75% of trucks sold were green. 27% of all sales were cars; 12.5% of cars sold were silver. 34% of all sales were convertibles; 24% of convertibles sold were red. Given that a person purchased a car, what is the probability that it was not silver?
What is this is impossible?
The expected value of rolling a 6-sided die is 3.5. Explain this in terms of the long run.
What is "If we roll the die a large number of times, we can expect the average of numbers rolled to be 3.5"?
I have a fair 26 sided die with the letters A-Z on it. If I roll it 5 times, what is the probability that I get only the letter P all 5 times?
(1/26)^5
You're in the kitchen!! In a pickleball tournament, I played 4 opponents. My probability of winning against the first one was 0.7; the second 0.4; the third 0.23; and the fourth 0.78. Is my tournament a binomial RV?
What is NO!
Apple produces 75% of all computers sold and 5% of their computers malfunction. Dell produces 8% of computers but 27% of them malfunction! Acer produces the rest with half of their computers malfunctioning. Given that a computer malfunctions, find the probability that it's an Acer.
When X = -40, P(X) = 0.12. When X = -30, P(X) = 0.04. When X = -20, P(X) = 0.05. When X = -10, P(X) = 0.17. When X = 0, P(X) = 0.62. Calculate the expected value, variance, and standard deviation for X.
What is E[X] = -8.7, Var[X] = 189.31, sd[X] = 13.759.
An iPod is set to play songs at random from the fifteen songs it contains in memory. Any song can be played at any time, even if it is repeated. There are 5 songs by Taylor Swift, 3 songs by Adele, 2 by Nicki Minaj, and 5 Zach Bryan. If the player has just played two songs in a row by Zach Bryan, what is the probability that the next song will also be by him?
What is 1/3?