Download Probability Intro

IM 9 Advanced: Introduction to Probability What is Probability? Part 1: Experimental Probability – Experiments Involving Chance Example: Lebron James shoots 100 free throws, and makes 89 of them. For the Lebron James free-­‐throw experiment above, list the following… a) number of trials: c) outcomes: b) frequency: d) relative frequency: Part 2: Probabilities from Data – Using Data to Estimate the Probability of an Event a. b. i. ii. iii. Part 3: Sample Space – The Sample Space of an Experiment is the Set of All Possible Outcomes Example: The sample space for rolling one die is 1, 2, 3, 4, 5, 6 . This is in the form of a list. One can also write the sample space as a grid or a tree diagram. Example: List the sample space for rolling two dice in the form of a grid. Example: List the sample space for flipping a coin 3 times in the form of a tree diagram. Part 4: Theoretical Probability – The Number of Ways an Event Can Occur Divided by the Total Number of Outcomes. Example: In the case where Lebron James is shooting free throws, the theoretical probability of him !
making a shot is !. This is because there are two possible outcomes, either he makes it or misses it, both are assumed to be equally likely to occur when talking about a theoretical probability. The !"
experimental probability of him making a shot would be !"" = .89. This is based on data. i) ii) Part 5: Compound Events – Calculating Probabilities for Combined Events Imagine that you simultaneously flip a fair coin and roll a fair number cube. 1. Use a grid to help you find the probability of getting a tail AND rolling a 6? 2. Now, what is the probability of flipping a coin and getting a tail? 3. What is the probability of rolling a die and getting a 6? 4. Multiply your probabilities from 2 and 3 above. Compare with your probability in 1. What do you notice? 5. Create a rule that allows you to find probabilities of certain compound events. Part 6: Selection with or without replacement – Putting Objects Back, or Not! a) b) i) iii) ii) iv) a) a) d) b) c) d) b) e) c) Part 7: Independent Events – Two Events Are Said to Be Independent if the Occurrence of One Event does NOT Affect the Outcome of the Other Looking back at previous examples in this packet, give two examples of independent events. 1. 2. Now, make up your own original situation that involves a compound probability event that would be considered independent. Part 8: Dependent Events – Two Events Are Said to Be Dependent if the Occurrence of One Event DOES Affect the Outcome of the Other Looking back at previous examples in this packet, give two examples of dependent events. 1. 2. Now, make up your own original situation that involves a compound probability event that would be considered dependent. Decide whether the problems below describe independent or dependent events, then solve them. Part 9: Venn Diagrams – A Useful to Avoid “Double Counting” Outcomes for an Event Example of “double counting”: Consider the experiment of rolling a single die. What is the probability of rolling an even number or a prime number? !
!
With double counting, the answer would be ! ! This is because there is a ! chance of rolling an !
even number (2, 4, 6) and a ! chance of rolling prime number (2, 3, 5). That doesn’t make sense! However, without double counting, the answer would be 5 6. Why is this correct? Use of a Venn Diagram: When there are more outcomes to consider, a Venn Diagram is useful for identifying the “overlapped” or “double counted” events. a) b) c) *Note: Mr. Galbraith reported that he gave NEITHER chocolates nor flowers for his wife’s last birthday Part 10: Problem Solving with Probability using Tree, Grid or Venn Diagrams In your notebook, use a grid, tree, or Venn diagram to help you solve the following. 1. A coin and a die are tossed simultaneously. Find the probability of getting: a. A tail and a 6 b. Neither a 2 nor a 6 c. A head and an odd number d. A tail or a 6 e. Neither a tail nor a 5 f. A head or an odd number 2. Suppose that a pair of dice is rolled. a. List the sample space for the experiment in that way you think is most effective. Think carefully and logically! b. Find the probability of getting i. Two 3s ii. A 5 and a 6 iii. A 5 or a 6 iv. At least one 6 v. Exactly one 6 vi. No sixes vii. A sum of 7 viii. A sum of 7 or 11 ix. A sum greater than 8 x. A sum of no more than 8 3. Bag A contains 4 red jellybeans and 1 yellow jelly bean. Bag B contains 2 red and 3 yellow jellybeans. A Bag is randomly selected by tossing a coin, then a jelly bean is selected from it. Determine the probability that the jelly bean selected is yellow. 4. Tennis start Boris gets his first serve in 72% of the time. If he gets his first serve in, he wins the point 85% of the time. If he does not get his first serve in, he only wins the point 50% of the time. Find the probability that Boris will win the next point he serves. 5. The medical records for a class of 30 children show whether they have previously had measles or mumps. 24 have has measles, 12 have had both and 26 have has measles or mumps. If one child from the class is selected at random, determine the probability that he or she has had: a. Mumps b. Mumps but not measles c. Neither mumps nor measles 6. At the local girls’ school, 65% of the students play netball, 60% play tennis, and 20% play neither sport. Determine the likelihood that a randomly selected student plays: a. Netball b. Netball but not tennis c. At one of these two sports d. Exactly one of these two sports.