IM3.7.5 Probability Rules
0. Notation and vocab from last time
1. Complement Rule
You’ve already used this informally, but let’s formalize it by writing a formula to practice our math notation. a. If the probability that my flight is on time is 0.78, what’s the probability that my flight is not on time? b. Formalize this idea by writing a formula for P(A')
2. Conditional Probability
We’ve also seen this one before, but let’s get them all in the same place.When a room is randomly selected in a downtown hotel, the probability that the room has a king-sized bed is 0.62, the probability that the room has a view of the town square is 0.43, and the probability that it has a king-sized bed and a view of the town square is 0.38. Let A be the event that the room has a king-sized bed, and let B be the event that the room has a view of the town square. a. What is the meaning of in this context?
2b. Two way table
2c. Venn Diagram
2d-f. Equation and independence
d. Below, write the equation for e. What is the condition for independence? f. Are these two events independent? Describe what your answer means in context.
3. Multiplication rule (for the intersection of independent events)
a. You're playing a game where you flip a coin and roll a die. Are these two events independent? b. What is the probability of getting a heads on the coin and a 6 on the die? c. Write a formula for if A and B represent independent events.
4. Addition rule (for the union of two events)
Josie will soon be taking exams in math and Spanish. She estimates that the probability she passes the math exam (M) is 0.9, and the probability that she passes the Spanish exam (S) is 0.8. She is also willing to assume that the results of the two exams are independent of each other. a. On paper, make a Venn diagram illustrating this situation.b. Using Josie’s assumption of independence, calculate the probability that she passes both exams. c. Find the probability that Josie passes at least one of the exams. (Hint: Passing at least one of the exams is passing math or passing Spanish.) d. Write a formula for finding .
5. Disjoint Events
Two events are said to be disjoint if they have no outcomes in common. a. Can you think of two events that are disjoint? b. What would a Venn diagram of two disjoint events look like? c. A set of cards consists of the following:- black cards showing squares - black cards showing circles - red cards showing X’s - red cards showing diamonds A card will be selected at random from the set. Find the probability that the card is black or shows a diamond. d. How is this related to the formula you wrote for number 4?