Theoretical and Experimental 11 2 Probability Section 11

Theoretical and Experimental 11 -2 Probability Section 11. 2 Theoretical and Experimental Probability Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Objectives Find theoretical probability of an event. Find the experimental probability of an event. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability _______is the measure of how likely an event is to occur. Each possible result of a probability experiment or situation is an ________. The ______is the set of all possible outcomes. An _____ is an outcome or set of outcomes. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Probabilities are written as fractions or decimals from 0 to 1, or as percents from 0% to 100%. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability __________have the same chance of occurring. When you toss a fair coin, heads and tails are equally likely outcomes. __________ are outcomes in a specified event. For equally likely outcomes, the _____________of an event is the ratio of the number of favorable outcomes to the total number of outcomes. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Example 1 A: Finding Theoretical Probability Each letter of the word PROBABLE is written on a separate card. The cards are placed face down and mixed up. What is the probability that a randomly selected card has a consonant? Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Example 1 B: Finding Theoretical Probability Two number cubes are rolled. What is the probability that the difference between the two numbers is 4? There are ____ possible outcomes. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Check It Out! Example 1 a A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability of the event? The sum is 6. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Check It Out! Example 1 b A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability of the event? The difference is 6. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Check It Out! Example 1 c A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability of the event? The red cube is greater. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability The sum of all probabilities in the sample space is 1. The _______of an event E is the set of all outcomes in the sample space that are not in E. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Example 2: Application There are 25 students in study hall. The table shows the number of students who are studying a foreign language. What is the probability that a randomly selected student is not studying a foreign language? Holt Algebra 2 Language Number French 6 Spanish 12 Japanese 3

Theoretical and Experimental 11 -2 Probability Example 2 Continued Use the complement. There are 21 students studying a foreign language. There is a ____ chance that the selected student is not studying a foreign language. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Example 3: Finding Probability with Permutations or Combinations Each student receives a 5 -digit locker combination. What is the probability of receiving a combination with all odd digits? Step 1 Determine whether the code is a permutation or a combination. Order is important, so it is a _________. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Example 3 Continued Step 2 Find the number of outcomes in the sample space. number Holt Algebra 2 number

Theoretical and Experimental 11 -2 Probability Example 3 Continued Step 3 Find the number of favorable outcomes. odd Holt Algebra 2 odd odd

Theoretical and Experimental 11 -2 Probability Example 3 Continued Step 4 Find the probability. The probability that a combination would have only odd digits is Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Check It Out! Example 3 A DJ randomly selects 2 of 8 ads to play before her show. Two of the ads are by a local retailer. What is the probability that she will play both of the retailer’s ads before her show? Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Experimental probability is often used to estimate theoretical probability and to make predictions. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Example 5 A: Finding Experimental Probability The table shows the results of a spinner experiment. Find the experimental probability. Number Occurrences 1 6 2 11 3 19 4 14 Holt Algebra 2 spinning a 4

Theoretical and Experimental 11 -2 Probability Example 5 B: Finding Experimental Probability The table shows the results of a spinner experiment. Find the experimental probability. Number Occurrences 1 6 2 11 3 19 4 14 Holt Algebra 2 spinning a number greater than 2

Theoretical and Experimental 11 -2 Probability Check It Out! Example 5 a The table shows the results of choosing one card from a deck of cards, recording the suit, and then replacing the card. Find the experimental probability of choosing a diamond. Holt Algebra 2

Theoretical and Experimental 11 -2 Probability Check It Out! Example 5 b The table shows the results of choosing one card from a deck of cards, recording the suit, and then replacing the card. Find the experimental probability of choosing a card that is not a club. Holt Algebra 2

11 -4 Compound Events Section 11. 4 Compound Events Holt Algebra 2

11 -4 Compound Events Objectives Find the probability of mutually exclusive events. Find the probability of inclusive events. Holt Algebra 2

11 -4 Compound Events A _______is an event that describes a single outcome. A _______is an event made up of two or more simple events. __________are events that cannot both occur in the same trial of an experiment. Rolling a 1 and rolling a 2 on the same roll of a number cube are mutually exclusive events. Holt Algebra 2

11 -4 Compound Events Holt Algebra 2

11 -4 Compound Events Example 1 A: Finding Probabilities of Mutually Exclusive Events A group of students is donating blood during a blood drive. A student has a having type O blood and a probability of having type A blood. Explain why the events “type O” and “type A” blood are mutually exclusive. Holt Algebra 2

11 -4 Compound Events Example 1 B: Finding Probabilities of Mutually Exclusive Events A group of students is donating blood during a blood drive. A student has a having type O blood and a probability of having type A blood. What is the probability that a student has type O or type A blood? Holt Algebra 2

11 -4 Compound Events Check It Out! Example 1 a Each student cast one vote for senior class president. Of the students, 25% voted for Hunt, 20% for Kline, and 55% for Vila. A student from the senior class is selected at random. Explain why the events “voted for Hunt, ” “voted for Kline, ” and “voted for Vila” are mutually exclusive. Holt Algebra 2

11 -4 Compound Events Check It Out! Example 1 b Each student cast one vote for senior class president. Of the students, 25% voted for Hunt, 20% for Kline, and 55% for Vila. A student from the senior class is selected at random. What is the probability that a student voted for Kline or Vila? Holt Algebra 2

11 -4 Compound Events ________are events that have one or more outcomes in common. When you roll a number cube, the outcomes “rolling an even number” and “rolling a prime number” are not mutually exclusive. The number 2 is both prime and even, so the events are inclusive. Holt Algebra 2

11 -4 Compound Events There are 3 ways to roll an even number, _____. There are 3 ways to roll a prime number, _____. The outcome “ 2” is counted twice when outcomes are added (3 + 3). The actual number of ways to roll an even number or a prime is _________. The concept of subtracting the outcomes that are counted twice leads to the following probability formula. Holt Algebra 2

11 -4 Compound Events Holt Algebra 2

11 -4 Compound Events Example 2 A: Finding Probabilities of Compound Events Find the probability on a number cube. rolling a 4 or an even number P(4 or even) = Holt Algebra 2

11 -4 Compound Events Example 2 B: Finding Probabilities of Compound Events Find the probability on a number cube. rolling an odd number or a number greater than 2 P(odd or >2) = There are 2 outcomes where the number is odd and greater than 2. Holt Algebra 2

11 -4 Compound Events Check It Out! Example 2 a A card is drawn from a deck of 52. Find the probability of each. drawing a king or a heart P(king or heart) = Holt Algebra 2

11 -4 Compound Events Check It Out! Example 2 b A card is drawn from a deck of 52. Find the probability of each. drawing a red card (hearts or diamonds) or a face card (jack, queen, or king) P(red or face) = Holt Algebra 2

11 -4 Compound Events Example 3: Application Of 1560 students surveyed, 840 were seniors and 630 read a daily paper. The rest of the students were juniors. Only 215 of the paper readers were juniors. What is the probability that a student was a senior or read a daily paper? Holt Algebra 2