Unit 8 Probability Quiz Review Ch. 9 Lessons 1, 2, 5, 6 and 7

9-1 Probability of Simple Events P(event) = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Probability is a number between 0 and 1 Near 0 =very unlikely Near 1 = very likely

9-1 Probability can be written as fraction, decimal, or percent Simplify all fractions Fraction to decimal Divide numerator by denominator Decimal to percent Multiply decimal by 100 (move decimal two places to right)

9-1 Eight cards are marked 3, 4, 5, 6, 7, 8, 9, and 10 such that each card has exactly one of these numbers. A card is picked without looking. Find each probability. Write each answer as a fraction, a decimal, and a percent. 1.) P(9) 2.) P(3 or 4) 3.) P(greater than 5) 4.) P(not 6)   

9-1 Complementary Events Two events in which either one or the other must happen, but they cannot happen at the same time The sum of the probability of an event and its complement is 1 or 100% Ex: A coin can either land on tails or not land on tails

9-1 At the Baltimore International Airport, 82% of the flights arrive on time. Suppose a flight that arrived at the airport is selected at random. What is the probability that the flight did not arrive on time? Write the answer as a fraction, percent, and decimal. Explain your reasoning. Write a sentence that explains how likely it is for a flight at the Baltimore airport to arrive on time.

9-2 Theoretical and Experimental Probability Theoretical: what should happen (what’s expected) Experimental: what actually happens in a probability experiment Compare the two probabilities by changing the fractions to decimals and writing a sentence They are close because one fraction is close to the other OR They are not close because there were not enough trials

9-2 A spinner that is divided into four equal sections is spun 100 times and it lands on green 32 times. Find the experimental probability of landing on green. Find the theoretical probability of landing on green. Compare the experimental probability to the theoretical probability.

9-2 Predict Future Events Find the probability from the original problem Simplify it Set up a proportion with new total at the bottom of the second fraction and solve for the missing part

9-2 Use the graph of a survey of 24 seventh-grade students asked to name their favorite hobby. What is the experimental probability that a student’s favorite hobby is roller skating or singing? Suppose 150 seventh-grade students were surveyed. How many can be expected to say that roller skating or singing is their favorite hobby?

9-5 Fundamental Counting Principle Using multiplication instead of a tree diagram to find the number of possible outcomes in a sample space If there are more than 2 events, continue to multiply event outcomes together to determine the total number of outcomes Show and label outcomes for each event! If finding the probability of an event, use FCP to find the total number of outcomes (denominator) Usually one favorable outcome (numerator)

9-5 Use the Fundamental Counting Principle to find the total number of outcomes for each situation Selecting one sweatshirt from a choice of five sweatshirts and one pair of pants from a choice of four pairs of pants Tossing a dime, a quarter, a penny, and rolling a number cube

probability it will be a 4-bedroom home with a The table shows the kinds of homes offered by a residential builder. If the builder offers a discount on one home at random, find the probability it will be a 4-bedroom home with a contemporary kitchen and an open porch. Is it likely or unlikely for this to occur? Number of Bedrooms Style of Kitchen Type of Porch 5-bedroom Mediterranean Open 4-bedroom Contemporary Screen 3-bedroom Southwestern  

9-6 Permutations An arrangement, or listing, of objects in which order is important Use the Fundamental Counting Principle to find the number of permutations Once something is chosen, it cannot be chosen again Use blanks for number of objects! If finding the probability of an event, find the permutation (total number of outcomes) first Usually one favorable outcome (numerator)

9-6 Use the Fundamental Counting Principle to find the total number of outcomes for each situation There are 4 passengers in a car. In how many ways can the passengers sit in the 4 passenger seats of the car? Mr. Bernstein owns 14 paintings, but has only enough wall space in his home to display three of them at any one time. How many ways can Mr. Bernstein display three paintings in his home?

9-6 Glen received 6 birthday cards. If he is equally likely to read the cards in any order, what is the probability he reads the card from his parents first and the card from his sister second?

9-7 Independent and Dependent Events Independent: when one event does not affect the outcome of the other event Ex: spinning a spinner and rolling a number cube Find the probability of each event as fraction and multiply them Simplify answer

9-7 Dependent: the outcome of the first event affects the outcome of the second event Ex: You have a bag of marbles. You pick one marble, DO NOT REPLACE IT, and pick another one Number of outcomes usually changes for the second event Find the probability of the first event FIRST, then the second event and multiply them Simplify answer

9-7 The two spinners at the right are spun. Find each probability. (Independent or Dependent?) P(less than 5 and B) P(odd and A)

9-7 There are three quarters, five dimes, and twelve pennies in a bag. Once a coin is drawn from the bag, it is not replaced. If two coins are drawn at random, find each probability. (Independent or Dependent?) P(a quarter and then a penny) P(two dimes)