Probabilities of Multiple Events

In summary, the first question is asking for the probability that Jeanie remembers at least one of the three errands, which can be calculated by subtracting the probability of her forgetting all three errands from 1. The second question is asking for the probability of someone being selected for jury duty in a small city for two consecutive years, which can be calculated by finding the product of the probabilities of being selected for each individual year.
  • #1
daewoo
25
0

Homework Statement


Hey, i need some help with these two probability questions

1)Jeanie is a bit forgetful and if she doesn't make a "to do" list the probability that she forgets some thing is supposed to do is .1. Tomorrow she intends to run three errands and she fails to write them on her hand.
c)what is the probability jeanie remembers at least one of the three errands?

2)In a small city approx 15% of those eligible are called for jury duty in anyone calendar year. People are selected at random from those eligible. The same individual cannot be called more than once in the same year. What is the probability that an eligible person in this city is selected 2 years? 3 years?

Homework Equations


not sure if the second one is a binomial probability distribution


The Attempt at a Solution


For the first question i did:
P(Jeanie remembers first errand but not second or third)
P(jeanie remembers first) X P(jeanie forgets second) x P(jeanie forgets third)
(1-0.1)(0.1)(0.1)= 0.009 I got that, but I'm not too sure if i did it right just hoping someone could double check.

For the second question i really actually don't know how to set this up, so i haven't had much luck.
 
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  • #2
What you did for the first one is wrong.

You have two different ways you can solve the problem.
(i) (Easy way) You could find the probability that she remembers none of the errands, and then the total probability will be 1 minus that number. (The negation of "at least 1" is "less than 1" (in that case it is exactly 0 since you cannot have a negative number of errands).
(ii) (Longer way) Break up into cases. Case 1: She remembers 1 errand (here you have three cases: 1. she remembers first, forgets other two; 2. she remembers second, forgets other two; 3. she remembers third, forgets other two. Then Case 2: She remembers 2 errands (here again you have three cases), and finally Case 3: She remembers all 3 errands. Then you will need to add up all the probabilities, and that would be your answer.

Both ways you should get the answer to be .999For the second problem. Could you state the exact wording of the problem? Are you wanting the probability that someone will be selected ONCE in two years, or are you looking at the probability of begin selected TWICE in two years?
 
  • #3
oh thanks for the help for the first one,

The second question asks what's the probability that a person will be selected once two years in a row, so he's selected once in the first year, and the second year he is selected again.
 
  • #4
What is the probability that he is selected for the first year? What is the probability that he is selected for the second year (does this depend on whether or not he was selected the first year?)?

The answer you get should be: .0225
 

1. What are case probability questions?

Case probability questions are a type of probability question that involves a specific scenario or case. These questions require you to use your knowledge of probability to determine the likelihood of a certain outcome or event occurring in a specific case or scenario.

2. How do you approach solving case probability questions?

To solve case probability questions, you should first carefully read the given scenario and identify the variables and events involved. Then, use your knowledge of probability rules and formulas to calculate the likelihood of the desired outcome. It may also be helpful to create a diagram or table to organize the information and visualize the problem.

3. What are some common mistakes to avoid when solving case probability questions?

One common mistake is to assume that all events are independent, when in reality they may be dependent on each other. Another mistake is to overlook key information or variables in the scenario. It is important to carefully read and understand the given scenario before attempting to solve the problem.

4. How can I improve my skills in solving case probability questions?

To improve your skills in solving case probability questions, it is important to practice regularly and familiarize yourself with different types of scenarios and questions. You can also review probability rules and formulas, and seek help from a tutor or teacher if needed.

5. Can real-life situations be represented as case probability questions?

Yes, real-life situations can be represented as case probability questions. For example, determining the probability of winning a game of chance or the likelihood of a certain outcome in a medical diagnosis can all be approached as case probability questions. Probability is a useful tool in understanding and predicting real-world events and situations.

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