Toss two coins 60 times. Record the number of heads in each trial, in a table.


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1 Coin Experiment When we toss a coin in the air, we expect it to finish on a head or tail with equal likelihood. What to do: Toss one coin 40 times. ecord the number of heads in each trial, in a table: Toss two coins 60 times. ecord the number of heads in each trial, in a table. Toss three coins 80 times. ecord the number of heads in each trial, in a table. Share your results for 1, 2, and 3 with several other students. Comment on any similarities and differences. Pool your results and find new relative frequencies for tossing one coin, two coins, and three coins. Be ready to share your results with the class. Questions on the homework? 1
2 POBABILITY CONTINUED Learning Target 3.2 Theoretical Probability Learning Target 3.3 Compound events C. THEOETICAL POBABILITY The likelihood of obtaining the outcome 2 would be: The likelihood of obtaining the outcome 2 or 5 would be: This is a mathematical or theoretical probability and it is based on what we theoretically expect to occur. It is the chance of that event occurring in any trial of the experiment. Theoretically, a coin toss showing heads should occur 1 every 2 times thrown. 2
3 SO HOW DO QUANTIFY IT A is the event. U is the sample space that event can occur in. So P(A) is the probability that that event can occur in the sample space U. EXAMPLE You have a bag of Jelly Beans and you randomly selected from the bag. It contains: Buttered Popcorn Coffee Boogers 1) Determine the probability of getting the booger jellybean? 2) What is the probability of not getting the coffee one? 3) What is the probability of getting a booger one or a coffee one? 4) what is the probability of getting a grape one? 3
4 YOU TY ON YOU OWN. STOP TALKING. GACE. An ordinary 8 sided die is rolled once. Determine the chance of: A) Getting a 6 B) P not 6 C) Getting a 1 or 2 D) Not getting a 1 or 2. COMPLEMENTAY EVENTS Two events are complementary if exactly one of the events must occur. If A is an event, then A is the complementary event of A, or not A. P(A) + P(A ) = 1 This reads, the probability of A occurring plus the probability of A not occurring equals 1. We can solve for each of the probabilities. P A = 1 P(A ) P A = 1 P A Example: Emma is going to the park. She has seen her friends at the park hanging out and rollerblading 23% of the time. What is the probability that Emma will not see her friends? 4
5 ANOTHE EXAMPLE! Use a 2D grid to illustrate the sample space for tossing a coin and rolling a 6 sided die simultaneously. From this grid, determine the probability of: a) Tossing a head b) Getting a Tail and a 5 c) Not Getting a tail or a 6. EXAMPLE 3 Draw a table of outcomes to display the possible results when two dice are rolled and the scores are added together. Determine the probability that the sum of the dice is 7. Find the probability that the dice will not add to be
6 D. COMPOUND EVENTS Consider the following problem: Box X contains 2 blue and 2 green balls. Box Y contains 1 white and 3 red balls. A ball is randomly selected from each of the boxes. Determine the probability of getting a blue ball from X and a red ball from Y What can we say about these two events happening? What do we do to interpret the 2D grid? W B B G G D. INDEPENDENT EVENTS We can see that the area highlighted is the possible outcomes and the total area is the universal set We can do this without drawing a 2D grid because they are independent compound events. two events for which the occurrence of each one does not affect the occurrence of the other, we call these independent events. P B and = P B P = 3 8 W B B G G 6
7 D. INDEPENDENT EVENTS EXAMPLE Franco went to the store to buy some vegetables for his pet rabbit. Before he went he found out that 1 carrots were dirty and may cause his rabbit to get 10 sick. He also discovered that 2 lettuce heads are dirty as well. Assuming that 9 he gets equal amounts of each vegetable; A) What are the chances that Franco will pull a dirty carrot and dirty lettuce? B) What are the chances of Franco not pulling a dirty vegetable? D. DEPENDENT EVENTS A dependent event happens when one even occurs that affects the following event. If event A effects event B, we would write: P A then B = P A P B, given that A has occurred Example: Suppose an urn contains 5 red and 3 blue tickets. One ticket is randomly chosen, its colour is noted, and it is then put aside. A second ticket is then randomly selected. If the first ticket was red, what would the probability the second is red? If the first ticket was blue, what would the probability be second is red? What is the probability that the first one was red and the second one is blue? =
8 E. USING A TEE DIAGAM Kareem is not having much luck with his motor vehicles. His car will only start 80% of the time and his motorcycle will only start 60% of the time. Are these dependent or independent events? Construct a tree diagram to illustrate his situation. Use the diagram to determine the chance that Both will start. Kareem can only use his car. First start Car MC start M M Car M M ADDING EVENTS If there is more than one outcome in an event then we need to add the probabilities of these outcomes. Example Two boxes each contain 6 petunia plants that are not yet flowering. Box A contains 2 plants that will have purple flowers and 4 plants that will have white flowers. Box B contains 5 plants that will have purple flowers and 1 plant that will have white flowers. A box is selected by tossing a coin, and one plant is removed at random from it. Determine the probability that it will have purple flowers using a tree diagram. We are trying to find P(purple flowers), therefore, this equals P(A and P) + P(B and P) You complete the exercise. 8
9 HW: 9CE C.1 #24 C.2 #2 C.3 #1,3 D.1 #1,2,6 D.2 #1,2,5 E #1,2,57 9
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