1. ## Conditional Probability

Hello to everyone. I am new in the forum and in the statistics at all. I have some homework to do and I can't figure it out. I am trying to do those tasks for second day but somewhere I miss something and I am not certain in my decisions. So I would like little help with those tasks and explanations if it is possible. Thank in you advance.

2. Let A denote the event that the midtown temperature in Lugano is 25C, and let B denote the event that the midtown temperature in Milan is 25C. Also, let C denote the event that the maximum of the midtown temperatures in Milan and in Lugano is 25C. If P(A) = .3, P(B) = .4, and P(C) = .2, nd the probability that the minimum of the two midtown temperatures is 25C.

3. Last summer I asked my neighbor to water a sickly plant while I was on vacation. Without water, it will die with probability .7; with water, it will die with probability .15. I was 89 percent certain that my neighbor will remember to water the plant. (a) What is the probability that the plant was alive when I returned? (b) If found the plant dead when I returned, what was the probability that my neighbor forgot to water it?

4. In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat.What is:
a) the probability that a randomly selected family owns both a dog and a cat?
b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?

2. ## Re: Conditional Probability

I'm unsure about the first question because I think the complement of event C is "The maximum temperature of the two cities is not 25C". So, i don't know how to get an equation in terms of minimum temperature. The second question involves the law of total probability. You are conditioning on whether the plant receives water or not. Part b) is Bayes' Rule. The third question requires writing P(Dog and Cat) in terms of conditional probability.

3. ## Re: Conditional Probability

Originally Posted by Buckeye
I'm unsure about the first question because I think the complement of event C is "The maximum temperature of the two cities is not 25C". So, i don't know how to get an equation in terms of minimum temperature. The second question involves the law of total probability. You are conditioning on whether the plant receives water or not. Part b) is Bayes' Rule. The third question requires writing P(Dog and Cat) in terms of conditional probability.
Yea the first one is the toughest for me..... I just can't get anything because of that maximum and minimum. About the second one I've done a) with the law of multiplication instead of the law of total probability and part b) was with the Bayes' Theorem. The third one was also quite confusing because I went for Bayes' Theorem... and law of total probability and got confused. Thank you very much for everything.

I would like to hear also other suggestions, especially for the first one

4. ## Re: Conditional Probability

Hint for the third question: If P(C|D)=P(D and C)/P(D) then isn't it true that P(C|D)*P(D)= P(D and C)? Similar argument for P(D|C)

Question one might be asking for P(A or B). In this case, there is a straightforward equation. The wording of the question is still awkward in my opinion.

5. ## Re: Conditional Probability

Ok, thank you very much.

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