1. PROBABILITY RULES – compound Events You roll two dice. What is the probability that you get a 5 on each die ?

2. PROBABILITY RULES – compound Events You roll two dice. What is the probability that you get a 5 on each die ? Suppose you have a bag of 6 colored gumballs; 3 green, 2 blue, and 1 red. What is the probability that you get green on the first draw, and then without replacing the first gumball, you get green again on the second draw?

3. PROBABILITY RULES – compound Events You roll two dice. What is the probability that you get a 5 on each die ? Suppose you have a bag of 6 colored gumballs; 3 green, 2 blue, and 1 red. What is the probability that you get green on the first draw, and then without replacing the first gumball, you get green again on the second draw? These scenarios are similar, but also differ on one important aspect.

4. PROBABILITY RULES – compound Events You roll two dice. What is the probability that you get a 5 on each die ? Suppose you have a bag of 6 colored gumballs; 3 green, 2 blue, and 1 red. What is the probability that you get green on the first draw, and then without replacing the first gumball, you get green again on the second draw? These scenarios are similar, but also differ on one important aspect. The fact that the first die had a 5 did not affect the outcome of the second die. The dice are independent of each other and one outcome will not change or have any effect on the outcome of the other die.

5. PROBABILITY RULES – compound Events You roll two dice. What is the probability that you get a 5 on each die ? Suppose you have a bag of 6 colored gumballs; 3 green, 2 blue, and 1 red. What is the probability that you get green on the first draw, and then without replacing the first gumball, you get green again on the second draw? These scenarios are similar, but also differ on one important aspect. The fact that the first die had a 5 did not affect the outcome of the second die. The dice are independent of each other and one outcome will not change or have any effect on the outcome of the other die. INDEPENDENT EVENTS When the occurrence or nonoccurrence of one event does NOT change the probability that the other event will occur.

6. PROBABILITY RULES – compound Events Now let us look at the gumball example. To begin with we have a total of 6 gumballs. When you remove one gumball and DO NOT replace it, you have changed the number of favorable outcomes and the total number of outcomes.

7. PROBABILITY RULES – compound Events Now let us look at the gumball example. To begin with we have a total of 6 gumballs. When you remove one gumball and DO NOT replace it, you have changed the number of favorable outcomes and the total number of outcomes. We had 6 gumballs, 3 of which are green. Once we pick a green, there are now only 5 gumballs remaining, two of which are green. This is called conditional probability and are dependent events. One occurrence affects the outcome of other events.

8. PROBABILITY RULES – compound Events

18. EXAMPLE : Andrew is 55 years old and the probability that he will be alive in 10 years is 0.72. Ellen is 35 years old and the probability that she will be alive in 10 years is 0.92. Assuming that the life span of one will have no effect on the life span of the other, what is the probability they will both be alive in 10 years ?

19. PROBABILITY RULES – compound Events

24. ADDITION rules : Another way to combine events is to consider the possibility of one event occurring OR another event occurring. This actually makes the event occurrence MORE likely.

25. PROBABILITY RULES – compound Events ADDITION rules : Another way to combine events is to consider the possibility of one event occurring OR another event occurring. This actually makes the event occurrence MORE likely. Consider a high school Biology class that has a combination of freshman thru seniors. There are 15 freshman, 8 sophomores, 6 juniors, and 2 seniors for a total of 31 students in the class. If we chose a student at random, what is the probability of choosing a freshman OR a sophomore ?

26. PROBABILITY RULES – compound Events

36. EXAMPLE : Laura is playing monopoly. On her next move she needs to throw a sum bigger than 8 on the two dice in order to land on her own property and pass Go. What is the probability of Laure rolling a sum greater than 8 ?

37. PROBABILITY RULES – compound Events EXAMPLE : Laura is playing monopoly. On her next move she needs to throw a sum bigger than 8 on the two dice in order to land on her own property and pass Go. What is the probability of Laure rolling a sum greater than 8 ? Solution : Since it is impossible to roll two numbers at one time, the events are mutually exclusive. The rolls greater than 8 are 9, 10, 11, and 12.

38. PROBABILITY RULES – compound Events

41. EXAMPLE : At Hopewell Industries, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are in the table below : EmployeeDemocrat (D)Republican (R)Independent (I)Row Total Executive (E) 534948 Production Worker ( W ) 6321892 Column Total 685517140

42. PROBABILITY RULES – compound Events EXAMPLE : At Hopewell Industries, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are in the table below : EmployeeDemocrat (D)Republican (R)Independent (I)Row Total Executive (E) 534948 Production Worker ( W ) 6321892 Column Total 685517140

43. PROBABILITY RULES – compound Events EXAMPLE : At Hopewell Industries, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are in the table below : EmployeeDemocrat (D)Republican (R)Independent (I)Row Total Executive (E) 534948 Production Worker ( W ) 6321892 Column Total 685517140

44. PROBABILITY RULES – compound Events EXAMPLE : At Hopewell Industries, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are in the table below : EmployeeDemocrat (D)Republican (R)Independent (I)Row Total Executive (E) 534948 Production Worker ( W ) 6321892 Column Total 685517140

45. PROBABILITY RULES – compound Events EXAMPLE : At Hopewell Industries, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are in the table below : EmployeeDemocrat (D)Republican (R)Independent (I)Row Total Executive (E) 534948 Production Worker ( W ) 6321892 Column Total 685517140

46. PROBABILITY RULES – compound Events EXAMPLE : At Hopewell Industries, all 140 employees were asked about their political affiliation. The employees were grouped by type of work, as executives or production workers. The results are in the table below : EmployeeDemocrat (D)Republican (R)Independent (I)Row Total Executive (E) 534948 Production Worker ( W ) 6321892 Column Total 685517140