Probability

2. "Flip a coin twice" Experiment: Flip a coin twice Outcomes: HH, HT, TH, TT Sample space: {HH, HT, TH, TT} Event: Both head and tails = {HH, TT} 3. "Roller a spinner" Experiment: Roll a spinner Outcomes: 1,2,3,4,5,6,7,8 Sample space: S = {1,2,3,4,5,6,7,8} Event: Even number = {2,4,6,8} Directions: Match the following with each letter on the probability line. B 1. There are 7 days in a week A. 0 (impossible) 2. Next year, the month after November has 30 days. B. 0.25 (unlikely) 3. Drawing a red card from a deck of cards C. 0.5 (equally likely) 4. Choosing the letter "M" from a bag that contains D. 0.75 (likely) magnets for each letter in the alphabet E. 1 (certain) 5. Drawing a number between 2 and 10 from a F. Outcome deck of cards. G. Probability 6. Yes, No H. Sample space 7. Tossing a fair coin twice I. Experiment 8. The result of a single trial of an experiment J. Event 9. Guessing the number of marbles in a container 10. Choosing the QUEEN of hearts from a deck of cards ACTIVITY NO.4: TREE DIAGRAM Counting the number of occurrences of an outcome using Table, Tree Diagram and Systematic Listing Example 1: When you toss a coin, there are 2 possible outcomes: "head" or "tail". List all the possible outcomes and how many possible outcomes are there for the experiment of tossing two coins (a 1 - peso coin and a 5 - peso coin)? Solution: The list of possible outcomes for the experiment is shown in the table below, 1-peso coin S.peso coin Outcome Head (H) Head (H) H H (both heads) Head (H) rail (T) H T (1-peso coin head, 5-pesos coin tail) Tail (T Head (H) T H (5-peso coin head, 1-pesos coin tail) Tail (T) rail (T) T T (both tails Listing the outcomes, we have HH, HT, TH, TT. The total number of possible outcomes is 4. Aside from using table, you can use a Tree Diagram to help you find the possible outcomes using branches to list choices. It is a simple way to represent the sequence of event. Using a tree diagram. START Toss #1 H T Toss #2ACTIVITY no.3: 2 - COLUMN FORM Probability The branch of Mathematics that deals with uncertainty is probability. Probability i how likely it is that an event will occur. The chance that something is going to happen. |ll---I-'+"-'_' impisssible unlikely equally likely likely certain M 1 s a measure or estimation of Impossible -- This means that something has absolutely no chance of happening. Example: If! had only 3 red marbles in a bag, then it would be impossible for me to pull a blue marble out of the bag. Certain - This means that something denitely will happen, without a doubt. Example: , If someone pushes me into a pool, then it is certain that I will get wet. Likely -- This means that something probably will happen. You couldn't promise that it would happen for sure, but you could say that you think it would happen. Example: IfI played a trumpet in a room full of sleeping people, then it is likely that they would wake up. Unlikely - This means that something probably won't happen. It might happen, but usually it will not. Example: My dad wa kes up very early almost every morning. It is unlikely that he would ever sleep until noon. Additional Terms: Activities such as tossing or ipping a coin which could be repeated over and over again an called outcomes. or picking a card from a standard deck of cards without looking d which have well-dened are called experiments. The results are Illusbation: When you roll a balanced die once, there are 6 even number includes 3 outcomes; these are 2,4, and 6. The set of all possible outcomes of an experiment is the sample space individual outcome is a sample point. Sample Space Sample Point V 7 Flipping two coins \" Rolling a die 1. 2. 3. 4. 5. 6 5 Rolling a coin and a die H1. H2, H3, H4. H5. H8 ' ' simultaneously 1'1, 1'2, T3, 1'4, T5, 75 T3 Examples 1. \"A die is rolled once and comes up with four" In this example, rolling a die Is the experiment. The sample space is S = {1,2 3 4 5 5} and coming I I I , up with four is the outcome. A possible event may be coming up with even numbers are 2 4 5 f I ' possible outcomes which are 1, 2, 3, 4, 5, or 6. Getting an "Getting an even number\" is called an event. or probability space; and each Ill lll Listing all the possible outcomes we have HH, HT, TH, TT. There are 4 total number of possible outcomes, Start Example 2: Use systematic listing in writing all the possible outcomes for the experiment in rolling a die. Determine the total number of outcomes Solution: In rolling a die we have 6 possible outcomes. They are 1, 2, 3, 4, 5, 6. Directions: Make a tree diagram to show all the possible outcomes Problem: Natalie is ordering a milk tea. She could have a small, medium or large milk tea. She has a choice of wintermelon, Okinawa or slated caramel. How many different choices of milk tea can she have? Solution