Probability Homework Help

[AnnaS]

Of the entire senior class 60% have completed their homework. 20% have completed thier homework and recieved perfect scores. Two people are selected at random. What's the probability that both of them have completed their homework and recieved perfect scores?

I know the 20% is overlapping with the 60%/ it's the 20% of kids that got perfect scores I need to work with...but....dooo IIii multiple .20 × .20 to account for the fact that the probability is supposed to be for TWO students ????

Right now my answer is 4%...that just doesn't seem right to me.

Thanks in advance

 

[JeffM]

Does the problem mention how many kids are in the class?

Is it 20% of those who completed their homework or 20% of the entire class?

Probability problems frequently require very careful reading of the problem.

 

[pka]

Of the entire senior class 60% have completed their homework. 20% have completed thier homework and recieved perfect scores. Two people are selected at random. What's the probability that both of them have completed their homework and recieved perfect scores?

Lets suppose that there are 100 students in the Sr. class. How many of those complete his/her homework?
Of those how many make a perfect score?
Using those numbers, what is the probability that a randomly selected senior completed his/her homework perfectly?
What about two?

 

[Dr.Peterson]

Of the entire senior class 60% have completed their homework. 20% have completed thier homework and recieved perfect scores. Two people are selected at random. What's the probability that both of them have completed their homework and recieved perfect scores?

I know the 20% is overlapping with the 60%/ it's the 20% of kids that got perfect scores I need to work with...but....dooo IIii multiple .20 × .20 to account for the fact that the probability is supposed to be for TWO students ????

Right now my answer is 4%...that just doesn't seem right to me.

Thanks in advance

JeffM's questions are crucial.

Since it doesn't say "20% OF THOSE have completed their homework and received perfect scores", I would expect it to mean that 20% of all the students.

Now, suppose there are only 5 in the class. Then 3 completed their homework (60% of 5), and 1 of those also got a perfect score (20% of 5). In this case, the probability that 2 randomly selected students got a perfect score is zero! But with a larger class, the answer would be different. (I'm assuming that there are really 2 (distinct) students selected, rather than "selecting two with replacement", which is not really selecting two.

You can't just multiply two 0.20's together unless they are selected independently, meaning with replacement. But maybe that's what they expect you to do. If there were millions of students, this would be close enough.

 

[pka]

JeffM's questions are crucial., That is not the case
Since it doesn't say "20% OF THOSE have completed their homework and received perfect scores", I would expect it to mean that 20% of all the students

It absolutely does say "20% have completed thier homework and recieved perfect scores. " that is a direct quote from the original post, miss-spelling and all. What else do you think that means? Say \(\displaystyle C\) means that a student completes all homework and \(\displaystyle A\) means that the completed homework is perfect . Do you understand what the Rev. Mr. Bayes's rule says? \(\displaystyle \mathscr{P}(A\cap C)=\mathscr{P}(A| C)\mathscr{P}( C)\)

 

[JeffM]

It absolutely does say "20% have completed thier homework and recieved perfect scores. " that is a direct quote from the original post, miss-spelling and all. What else do you think that means? Say \(\displaystyle C\) means that a student completes all homework and \(\displaystyle A\) means that the completed homework is perfect . Do you understand what the Rev. Mr. Bayes's rule says? \(\displaystyle \mathscr{P}(A\cap C)=\mathscr{P}(A| C)\mathscr{P}( C)\)

Yes, that is what the original post said, misspellings and all. It may, however, not reflect what was said in the question presented to the original poster. Notice that, in addition to misspellings, the original post did not bother to identify how many students were in the class. Unless the random choice is with replacement, a point not mentioned in the original post, the probability required cannot be calculated exactly without knowing the number of students in the class. Moreover, the language on overlap is not a model of clear exposition. Therefore, I see no reason to presume that the original poster's paraphrase replicates what was in fact asked.

One of the main reasons to ask students to give the complete text of an exercise is that students frequently do not understand the problem fully. Consequently, their paraphrases are often wrong. The whole point of word problems is to teach how to determine what are the mathematically relevant facts from a conglomeration of relevancies and irrelevancies.

So, despite what the original poster said, I still think it is crucial to confirm that the student understood what the actual but unspecified problem said. The student will not find it helpful if we give the right answer to the wrong problem.