- Let A and B be events such that, P(A) = 0.3, P(B) = 0.6, P(A ⋂ B) = 0.2 Find a.P(A ⋃ B)
- P(A|B)
- P(B|A)

- According to a survey of hikers on a trail, 50% of the hikers like carrots (C) and 30% like broccoli (B). 20% like both. Write the following in terms of the events and assume random selection:
- Find the probability that a hiker likes carrots or broccoli
- If a hiker likes broccoli, find the probability that he likes carrots
- Find the probability that a hiker that likes carrots also likes broccoli.

- Find the probability that the sum of two die will be less than 7, given that the first die is a 5. Let A = “ sum of toss of two die is < 7.” B = “first die tossed was a 5”.

- Mason students on each campus were asked: Where were you born? The results are summarized below:

Campus | Virginia(V) | Other(O) | International (I) | Total |

Fairfax(F) | 200 | 50 | 80 | 330 |

Arlington(A) | 60 | 30 | 20 | 110 |

Sci-Tech(S) | 75 | 40 | 15 | 130 |

Total | 335 | 120 | 115 | 570 |

Assume Random Selection. Note: Your answers should use probability notation such as P(A) =

110/570 = .193, and always be phrased in terms of the given events such as: P(F|V)

- What is the probability of selecting a student who was born in Virginia?
- If the student selected is a Fairfax student, what is the probability that the student was born in Virginia
- What is the probability of student that was born in another state is an Arlington student?
- Given the student selected is an Arlington student, what is the probability that the student was not born in Virginia?
- Are birth place and campus independent events? Use the formula for independent events.

- There is a 40% chance that you will pass the final. There is a 45% chance that if you pass the final you will pass the course. There is a 80% chance that if you don’t pass the final, you won’t pass the course. Use probability notation. e.g. If F = “Pass the Final” and C= “Pass the Course”, P(F)= .40 P(C|F) =.45

Drawing a tree diagram may help you with this problem. What is the probability that you will pass the course?

- Using the data in problem #5, answer these questions (phrase each in terms of events (F, C), Union, Intersection, Complement):
- If you pass the course, what is the probability you passed the final?
- If you did not pass the course, what is the probability that you did not pass the final?