Term 2C Course Outline - Statistics and Probability PDF

T e rm 2C o u r s e O u t l i n e. Statistics and Probability. Sets and Probability Review of Sets and Venn Diagram Simple Probability ○ Theoretical Probability ○ Experimental Probability Compound Probability ○ Mutually and Non-Mutually Exclusive Events ○ De...

T e rm 2C o u r s e O u t l i n e. Statistics and Probability. Sets and Probability Review of Sets and Venn Diagram Simple Probability ○ Theoretical Probability ○ Experimental Probability Compound Probability ○ Mutually and Non-Mutually Exclusive Events ○ Dependent and Independent Events Statistics Review of Measures of Central Tendency Measures of Position of Grouped and Ungrouped Data ○ Median ○ Percentile ○ Quartile ○ Decile T e rm 2C o u r s e O u t l i n e Polynomial Expressions, Equations, and Functions Polynomial Expressions, Equations, and Functions Basic Concepts of Polynomials Division of Polynomials ○ Long Division ○ Synthetic Division Polynomial Equations Polynomial Functions (Applications and Graphs) Polynomial Expressions, Equations, and Functions Theorems on Solving Polynomial Equations o Remainder Theorem o Factor Theorem o Fundamental Theorem of Algebra o Rational Root Theorem o Multiplicity of Roots o Lower/Upper Bound Theorem o Quadratic Surd Theorem o Descartes’ Rule of Signs  Term 2 Cycle 1 UNIT III. Sets, Sample Space, and Experiments. Introduction to Probability \ Essential Question: H o w c a n w e u s e c o u n tin g te c h n iq u e s a n d p r o b a b ility to fo r m u la te c o n c lu s io n s a n d Learning Targets: d is c u s s io n , A t th e e n d o f th is o I c a n r e c a ll th e u n io n a n d in te r s e c tio n o f s e ts. o I c a n d e fin e p r o b a b ility a n d te r m s r e la te d to it. o I c a n d iffe r e n tia te s im p le fr o m. Have you ever wondered… What are your odds of winning the lottery? How likely it is to rain tomorrow? What is the probability that you will pass the entrance exam? Probability is the likelihood of an event to occur or happen. Concept Formation The probability of an event must lie between 0 and 1, inclusive. 0 ≤ 𝑃(𝐸) ≤ 1 This implies that the closer the probability of an event is to 1, the more likely the event is to happen. Terms Related to Probability ▪ An experiment refers to any situational activity that involves chance. It can be in the form of making observations or taking measurements. Common experiments are tossing a coin or rolling a die. ▪ Outcomes refers to any possible result of an experiment. ▪ Sample space refers to list of all possible outcomes. ▪ Events refers to any subset of sample space. It also refers to any collection of outcomes of an experiment. Examples Determine the sample space and outcomes, then give an example of event for each experiment. Experiment Outcomes Sample Space (S) Event (E) Event that an even Rolling a number appears 1, 2, 3, 4, 5, or 6 S = {1, 2, 3, 4, 5, 6} Die 𝑬 = {𝟐, 𝟒, 𝟔} Event that it lands on Tossing a heads Heads or Tails S = {Heads, Tails} Coin 𝑬 = {Heads}  Types of Probability Experimental Theoretical If an experiment is performed several Let S be the sample space of an experiment in times, the experimental probability that which all outcomes are equally likely, and let E be an event E will occur is given by the ratio: an event. Then the theoretical probability of E is: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑒𝑣𝑒𝑛𝑡 𝐸 𝑜𝑐𝑐𝑢𝑟𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟 𝑃 𝐸 = 𝑃 𝐸 = 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 REMEMBER: BASED ON TRIALS REMEMBER: TRUE PROBABILITY Experimental Probability A die is rolled 100 times and the results are recorded in the table below. Find the experimental probability of getting a 2. OUTCOME 1 2 3 4 5 6 FREQUENCY 15 18 21 16 11 19 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑒𝑣𝑒𝑛𝑡 𝐸 𝑜𝑐𝑐𝑢𝑟𝑠 𝑃 𝐸 = 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠 18 9 What will be the answer if we 𝑃 𝐸 = = 100 50 use theoretical probability? Theoretical Probability Suppose you roll a fair die. What is the probability of getting a 2? Sample Space = {1, 2, 3, 4, 5, 6} Solution: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟 𝑃 𝐸 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 1 𝑃 𝑔𝑒𝑡𝑡𝑖𝑛𝑔 𝑎 2 = 6 𝟏 What is the probability of getting a number more than 4? 𝟑 Theoretical Probability A deck of cards has 52 cards divided into two colors (black and red). There are four (4) suits in a deck: Heart, Diamond, Clubs, and Spade; and each suit has thirteen (13) cards: from Ace to King. Theoretical Probability If a card is selected randomly, determine the probability of getting: a. A red card? b. A queen card? c. A spade card? d. A number card? e. A letter card? f. A face card? Theoretical Probability If a card is selected randomly, determine the probability of getting: 𝟐𝟔 𝟏 a. A red card? = 𝟓𝟐 𝟐 𝟒 𝟏 b. A queen card? = 𝟓𝟐 𝟏𝟑 c. A spade card? 𝟏𝟑 𝟏 = 𝟓𝟐 𝟒 Theoretical Probability If a card is selected randomly, determine the probability of getting: 𝟑𝟔 𝟗 d. A number card? = 𝟓𝟐 𝟏𝟑 𝟏𝟔 𝟒 e. A letter card? = 𝟓𝟐 𝟏𝟑 f. A face card? 𝟏𝟐 𝟑 = 𝟓𝟐 𝟏𝟑 Theoretical Probability A box contains 4 red marbles, 5 yellow marbles, and 3 green marbles. If a marble is picked at random from the box, what is the probability that the marble picked is yellow? Solution: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 𝑐𝑎𝑛 𝑜𝑐𝑐𝑢𝑟 𝑃 𝐸 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 5 𝑃(𝑦𝑒𝑙𝑙𝑜𝑤 𝑏𝑎𝑙𝑙) = 4+5+3 𝟓 𝑃(𝑦𝑒𝑙𝑙𝑜𝑤 𝑏𝑎𝑙𝑙) = 𝟏𝟐 Think about this… A box contains 4 red balls, 5 yellow balls, and 3 green balls. If a ball is picked at random from the box, find the probability that a ball picked is a) a yellow ball? Simple Event b) a yellow or red ball? Compound Event Compare the two events. Remember Simple Event refers to an event with single outcome. Compound Events refer to events with more than one possible outcomes. TYPES OF COMPOUND EVENTS ❑ Mutually Exclusive Events ❑ Non-Mutually Exclusive Events ❑ Independent Events ❑ Dependent Events Activity: Union and Intersection of Sets Instructions: 1. Bring out your MLD. 2. Go to Canvas – Cycle 1 Module 3. Look for the activity – Recall: Union and Intersection of Sets 4. Follow the indicated instructions. 5. Explore, answer, and submit the activity.  Union and Intersection of Sets Union of Sets (A U B) Intersection of Sets (A ∩ B) The union of set A and set B is the The intersection of two sets A set whose elements are those which and B is the set whose elements belong to set A OR to set B, OR to are common to Set A AND Set B. both sets.