Chapter 8 Homework

  1. 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)
    1. P(A|B)
    2. P(B|A)

 

  1. 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:
    1. Find the probability that a hiker likes carrots or broccoli
    2. If a hiker likes broccoli, find the probability that he likes carrots
    3. Find the probability that a hiker that likes carrots also likes broccoli.

 

 

  1. 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”.

 

  1. 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) 2005080330
Arlington(A) 603020110
Sci-Tech(S) 754015130
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)

 

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

 

 

  1. 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?

 

 

 

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

 

 

Last Updated on October 22, 2019

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