Probability, Random Variables, and Probability Distributions

If it's known that after five patients were treated without reaction to a new medication, there was an approximately 10% chance that this could occur under normal conditions, what's implied about the single-trial reaction rate?

Which function is used to calculate the probability of a geometric random variable Y being equal to a specific value k?

If a player free-throw shooter succeeds % but misses several times in a row during a game, would this imply anything about their true shot-making skill level?

When researching consumer behavior patterns, if an analyst estimates that customers make purchases on average once every eight visits to an online store, what is the probability that a purchase will occur on any given visit?

A car salesperson sells cars at a rate where about fifteen percent are returned within thirty days due to buyer remorse. If she sells eight cars in January, what is the likelihood that exactly none come back?

If a geometric random variable has a probability of success of 0.3 on each trial, what is the probability of needing exactly 5 trials to achieve the first success?

What would you expect from many repetitions when considering an experiment following geometric distribution with $p = 0.5$?

What is the probability that a test will require more than 10 components to be tested before detecting a defect, given that the probability of a component failure is set at 0.111?

What is the expected value of trials needed for a basketball player with a free throw success rate of $p = \frac{1}{5}$ to make her first basket?

What is the possible range of values for a geometric random variable?