11.3 and 11.4: Probability Rules

Key Vocabulary  Independent events: The outcome of one event does not affect the outcome of another  Dependent events: The outcome of one event does affect the outcome of another  Mutually exclusive events: Events that can not both be true (occur).

Probability of A and B

What is the probability of flipping three heads in a row?

If a multiple choice test has 5 possible answers, what are the chances that you will guess 3 answers in a row correctly?

If you are dealt 3 cards in a row from a standard deck of playing cards, what is the probability they are all face cards?

What is the probability of rolling doubles when rolling two 10-sided dice? Rolling doubles twice in a row?

A bag contains 3 red and 6 blue marbles Suppose you take two marbles from the bag (without replacement). Determine the probability that: 1. Both are red 2. One is red and one is blue

Probability of A or B

Suppose a student can only take one elective class. 26% of students take Yoga and 43% of students take Nap Class. What is the probability that a student chosen at random is taking Yoga or Nap Class?

Suppose you choose one of theses shapes at random. What is the probability the shape is green OR a rectangle?

Suppose you draw a card from a standard deck of 52 cards Determine the probability the card is a King or a Heart

Birthday problem In a group of 3 people, what is the probability that at least two of them have the same birthday?

Birthday problem cont. In a group of 10 people, what is the probability that at least two of them have the same birthday?

Birthday problem cont. How many people must be in a group in order for this probability to exceed 40%?

Here’s a table of the birthday problem I stole from Wikipedia:

Monty Hall! Lets play a game!

Conditional Probability

Using a table A group of math and history specialists were surveyed. Determine the probability that a randomly selected person in this group: 1. Has a Master’s degree, given that s/he studied math. 2. Studied math, given that s/he has a Bachelor’s degree DegreeNumber of people Bachelor’s of Mathematics11 Master’s of Mathematics16 Bachelor’s of History15 Master’s of History3

Venn Diagrams In a group of 20 math teachers, 7 are wearing button-down shirts, 9 are wearing sweater vests, and 5 are wearing both button-down shirts AND sweater vests. Determine the probability that a randomly chosen teacher: 1. is wearing a sweater vest, but not a button-down? 2. is wearing a button-down, given that s/he is wearing a sweater vest

Tree diagrams On any given day, there is a 60% chance that Mr. Propri will watch Frozen. If he watches it, there is an 80% chance that he will cry (only during the sad parts). If he doesn’t watch it, there is still a 20% chance that he will cry just thinking about it. 1. What is the probability that Mr. Propri cried, given that he watched Frozen? 2. What is the probability that Mr. Propri watched Frozen, given that he cried yesterday?

When Mr. Cawelti plays Halo, there is a 70% chance that he will win. If he wins, there is a 20% chance that the opposing team will call him a “noob”. If he loses, there is a 60% chance the opposing team will call him a noob. Determine the probability that he won, given that he was called a noob.

Let’s look at the Monty Hall Problem again

Oh “Craps”! The dice game Craps is played by rolling 2 dice. If the player rolls a seven or eleven on the first roll they win. If they roll a 2,3, or 12 they lose. If they roll a 4,5,6,8,9, or 10 that number becomes “marked”. The player must then roll that “marked” number again before they roll a seven to win. If they roll a seven before they roll their “marked” number again they lose.

What are the chances of losing on the first roll?

What are the chances of winning on the first roll?

Given that a player has won on their second roll, what is the probability they rolled a 10 first?

What is the probability of not rolling a seven in 7 rolls?

What is the probability of winning if your marked roll is a four?