Tree-Top Tactics
This type of diagram is used to map sequential events and their probabilities.
What is a tree diagram?
A variable that takes numerical values describing the outcomes of a random process.
What is a random variable?
Adding a constant c to every value shifts the mean and quartiles by c, but leaves the range, IQR, shape, and this spread measure unchanged.
What is standard deviation?
The four conditions that define a geometric setting.
What are Binary, Independent, First Success, and the same probability of success for each trial?
Conditions for a binomial setting.
What are binary, independent, fixed number of trials, and the same probability of success on each trial?
The sum of the probabilities of all the terminal branches of a complete tree must equal this value.
What is 1?
A random variable that takes a fixed set of possible values with gaps between them.
What is a discrete random variable?
Multiplying every value by k multiplies the mean, median, quartiles, and standard deviation, but leaves this unchanged.
What is shape?
A geometric random variable counts this.
What is the number of trials until the first success?
A binomial random variable counts this.
What is the number of successes in n trials?
The second-level branch probabilities on the tree diagram represent this kind of probability.
What are conditional probabilities?
The formula for the expected value of a discrete random variable.
What is E(X) = Σ (x * P(x))?
If X and Y are independent, this is the formula for the standard deviation of S = X + Y.
What is √ (σx^2 + σy^2)
Shape & modality of every geometric distribution.
What is right-skewed and unimodal?
The symmetry of a binomial distribution depends on these two parameters.
What are n(number of trials) and p(probability of success on each given trial)?
At a track and field meet, every athlete is screened for illegal PEDs. 2% of athletes actually use illegal PEDS. If an athlete uses illegal PEDS, the lab returns a positive result 99% of the time. If an athlete is clean, the test returns a false positive 3% of the time. If a randomly selected athlete’s test comes back positive, find the probability that this athlete is using an illegal PED.
What is 0.402?
Shak buys a scratch-off lottery ticket that costs $5. If the ticket wins, he can win 50 dollars. If the ticket loses, he does not win any money. According to the lottery’s website, 2% of all tickets are winners. Find the expected value of buying a scratch-off lottery ticket.
What is -$4?
Jason’s bakery tracks the number of loaves of sourdough bread he sells every day, X. His research shows that the mean = 80, with a standard deviation of 12. Every loaf earns the bakery $4 in revenue, but the bakery also pays a $150 daily overhead for rent, utilities, etc. Find the mean and SD of the net revenue.
What is mean = $170 & standard deviation = $48?
The probability formula for geometric distributions.
What is P(X) = p(1-p)^(x-1)
The probability formula for binomial distributions.
What is P(X) = (n choose x) * p^x * (1-p)^(n-x)
Draw a Tree Diagram to solve this problem: A community college has built a new building for STEM-related fields and is seeing what majors want to have their classes in this new building. There are Engineers, Pre-Med, and the other two majors, Biology and Chemistry. Of the STEM Majors who want to be in this new building, 15% are engineering majors, 15% are pre-med majors, and the rest are the other STEM majors. The new “Jason Broome” labspace is constructed inside, with 40% of Engineering majors wanting this workspace, 10% of Pre-Med students wanting it, and 8% of the other majors wanting it. What is the probability that a randomly selected student of the “Jason Broome” labspace is an engineering major?
What is 0.46?
Will starts a candy shop that fills gift bags that contain two types of sweets: gummy bears and truffles. Let G = the number of gummy bears in a bag with a mean of 50 and an SD of 8. Let C = the number of chocolate truffles in a bag, with a mean of 30 and a SD of 5. Will sells each gummy bear for $0.2 and each truffle for $0.5. Define the bag’s total revenue as R. Find the expected revenue E(R) and standard deviation SD(R).
E(R) = $25
SD(R) = $2.97
Shivank’s streaming company sells two different subscription plans. On any given day, the number of Basic subscriptions sold, B, has a mean of 30 and a standard deviation of 5. The number of premium subscriptions sold, P, has a mean of 20 and a standard deviation of 4. The revenue per Basic subscription is $10 and $25 per Premium Subscription. Find the expected total revenue and standard deviation.
Russell Westbrook, a professional basketball player for the Denver Nuggets, has a 77.2% chance of making any given free throw. Assume each free throw is independent. Find the probability that Westbrook misses five free throws in a row before his first make.
What is 0.000476?
Ms. Tindall gives a test that has 15 multiple-choice questions, with four options for each question. Colin, who did not study, has to guess on each question. Find the probability of Colin getting more than half correct.
What is 0.0173?