Do Now: Copy down new vocab for 13.5 compound event- consists of two or more simple events independent events- the probability of the first event does not effect the probability of the second. dependent events- the probability of the first event changes the probability of the second conditional probability- the probability of an event under the condition that some preceding event has occurred. Vocabulary
A. A die is rolled, and then a second die is rolled. Identify Independent and Dependent Events Determine whether the event is independent or dependent. Explain your reasoning. A. A die is rolled, and then a second die is rolled. Answer: Example 1
A. A die is rolled, and then a second die is rolled. Identify Independent and Dependent Events Determine whether the event is independent or dependent. Explain your reasoning. A. A die is rolled, and then a second die is rolled. Answer: The two events are independent because the first roll in no way changes the probability of the second roll. Example 1
Identify Independent and Dependent Events Determine whether the event is independent or dependent. Explain your reasoning. B. A card is selected from a deck of cards and not put back. Then a second card is selected. Answer: Example 1
Identify Independent and Dependent Events Determine whether the event is independent or dependent. Explain your reasoning. B. A card is selected from a deck of cards and not put back. Then a second card is selected. Answer: The two events are dependent because the first card is removed and cannot be selected again. This affects the probability of the second draw because the sample space is reduced by one card. Example 1
Determine whether the event is independent or dependent Determine whether the event is independent or dependent. Explain your reasoning. A. A marble is selected from a bag. It is not put back. Then a second marble is selected. A. independent B. dependent Example 1
Determine whether the event is independent or dependent Determine whether the event is independent or dependent. Explain your reasoning. A. A marble is selected from a bag. It is not put back. Then a second marble is selected. A. independent B. dependent Example 1
Determine whether the event is independent or dependent Determine whether the event is independent or dependent. Explain your reasoning. B. A marble is selected from a bag. Then a card is selected from a deck of cards. A. independent B. dependent Example 1
Determine whether the event is independent or dependent Determine whether the event is independent or dependent. Explain your reasoning. B. A marble is selected from a bag. Then a card is selected from a deck of cards. A. independent B. dependent Example 1
Concept
Probability of Independent Events EATING OUT Michelle and Christina are going out to lunch. They put 5 green slips of paper and 6 red slips of paper into a bag. If a person draws a green slip, they will order a hamburger. If they draw a red slip, they will order pizza. Suppose Michelle draws a slip. Not liking the outcome, she puts it back and draws a second time. What is the probability that on each draw her slip is green? These events are independent since Michelle replaced the slip that she removed. Let G represent a green slip and R represent a red slip. Example 2
Probability of independent events Draw 1 Draw 2 Probability of independent events Answer: Example 2
Probability of independent events Draw 1 Draw 2 Probability of independent events Answer: So, the probability that on each draw Michelle’s slips were green is Example 2
LABS In Science class, students are drawing marbles out of a bag to determine lab groups. There are 4 red marbles, 6 green marbles, and 5 yellow marbles left in the bag. Jacinda draws a marble, but not liking the outcome, she puts it back and draws a second time. What is the probability that each of her 2 draws gives her a red marble? A. 12.2% B. 10.5% C. 9.3% D. 7.1% Example 2
LABS In Science class, students are drawing marbles out of a bag to determine lab groups. There are 4 red marbles, 6 green marbles, and 5 yellow marbles left in the bag. Jacinda draws a marble, but not liking the outcome, she puts it back and draws a second time. What is the probability that each of her 2 draws gives her a red marble? A. 12.2% B. 10.5% C. 9.3% D. 7.1% Example 2
Concept
Probability of Dependent Events EATING OUT Refer to Example 2. Recall that there were 5 green slips of paper and 6 red slips of paper in a bag. Suppose that Michelle draws a slip and does not put it back. Then her friend Christina draws a slip. What is the probability that both friends draw a green slip? These events are dependent since Michelle does not replace the slip she removed. Let G represent a green slip and R represent a red slip. Example 3
Probability of dependent events After the first green slip is chosen, 10 total slips remain, and 4 of those are green. Simplify. Answer: Example 3
Probability of dependent events After the first green slip is chosen, 10 total slips remain, and 4 of those are green. Simplify. Answer: So, the probability that both friends draw green slips is or about 18%. Example 3
LABS In Science class, students are again drawing marbles out of a bag to determine lab groups. There are 4 red marbles, 6 green marbles, and 5 yellow marbles. This time Graham draws a marble and does not put his marble back in the bag. Then his friend Meena draws a marble. What is the probability they both draw green marbles? A. B. C. D. Example 3
LABS In Science class, students are again drawing marbles out of a bag to determine lab groups. There are 4 red marbles, 6 green marbles, and 5 yellow marbles. This time Graham draws a marble and does not put his marble back in the bag. Then his friend Meena draws a marble. What is the probability they both draw green marbles? A. B. C. D. Example 3
Students who draw odd numbers will be on the Red team. Conditional Probability Mr. Monroe is organizing the gym class into two teams for a game. The 20 students randomly draw cards numbered with consecutive integers from 1 to 20. Students who draw odd numbers will be on the Red team. Students who draw even numbers will be on the Blue team. If Monica is on the Blue team, what is the probability that she drew the number 10? Example 4
Let A be the event that an even number is drawn. Conditional Probability Read the Test Item Since Monica is on the Blue team, she must have drawn an even number. So you need to find the probability that the number drawn was 10, given that the number drawn was even. This is a conditional problem. Solve the Test Item Let A be the event that an even number is drawn. Let B be the event that the number drawn is 10. Example 4
Draw a Venn diagram to represent this situation. Conditional Probability Draw a Venn diagram to represent this situation. There are ten even numbers in the sample space, and only one out of these numbers is a 10. Therefore, the P(B | A) = The answer is B. Example 4
Mr. Riley’s class is traveling on a field trip for Science class Mr. Riley’s class is traveling on a field trip for Science class. There are two busses to take the students to a chemical laboratory. To organize the trip, 32 students randomly draw cards numbered with consecutive integers from 1 to 32. Students who draw odd numbers will be on the first bus. Students who draw even numbers will be on the second bus. If Yael will ride the second bus, what is the probability that she drew the number 18 or 22? A. B. C. D. Example 4
Mr. Riley’s class is traveling on a field trip for Science class Mr. Riley’s class is traveling on a field trip for Science class. There are two busses to take the students to a chemical laboratory. To organize the trip, 32 students randomly draw cards numbered with consecutive integers from 1 to 32. Students who draw odd numbers will be on the first bus. Students who draw even numbers will be on the second bus. If Yael will ride the second bus, what is the probability that she drew the number 18 or 22? A. B. C. D. Example 4
Concept
Check your understanding
HOMEWORK P. 951 # 6- 30 even