Games of Chance

Compute coin-toss probabilities:

32 coin tosses

Compute dice probabilities:

5 dice

Compute odds for a poker hand:

poker full house

Analyze a bet in roulette:

bet the corner at roulette

Analyze a wager:

8:5 odds, bet 97 euros

Get lottery odds:

lottery

Bernoulli Trials

Compute probabilities for a sequence of trials:

probability of 8 successes in 14 trials with p=.6

Analyze waiting-time probabilities:

number of trials until 15th success

Find the probability of a run:

streak of 12 successes in 40 trials

Birthday Probabilities

Compute the probability of shared birthdays in a group of people:

birthday paradox 50 people

Specify the number of possible birthdays:

birthday paradox, 4 people, 100 possible birthdays

Compute the probability of shared birthdays for a given interval:

chance 3 people share a birthday

probability 5 people were born on the same day of the week

probability 2 people born in same month

Probability Formulas

Compute the probability of a union of events:

probability of the union of three events

Compute a conditional probability:

conditional probability formula

Compute the probability of a complement:

probability of a complement

Probability Distributions

Compute properties of a probability distribution:

Poisson distribution

Specify parameters for a distribution:

normal distribution, mean=0, sd=2

Compute a particular property:

standard deviation of Student t, 17 degrees of freedom