Question 1127381: Use the following set of 29 numbers to answer the questions.
23,23,28,30,34,36,36,37,39,40,43,49,50,55,55,55,57,62,68,71
,74,74,78,82,86,86,89,89,89
a). Let event B=odd number and let event C= less than the median. Calculate P(B|C) as a fraction in lowest terms.
b).Calculate P(C|B) as a fraction in lowest terms.
please show work
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The median of the set is 55. Since the middle three numbers are all 55, there are 13 numbers less than the median and 13 greater.
The conditional probability P(B|C) means we are looking only at the numbers that are less than the median (C) and finding how many of them are odd (B). Of the 13 numbers less than 55, 5 of them are odd. So
ANSWER (a): P(B|C) = 5/13.
The conditional probability P(C|B) means we are looking at only the odd numbers (B) and finding how many of them are less than the median (C). Of the 29 numbers, 13 are odd; 5 of them are less than the median. So with this set of numbers
ANSWER (b): P(C|B) = 5/13.
Note the two probabilities are the same. But they are calculated differently.
In both probabilities, the numerator of the probability fraction is the number of numbers that are both odd and less than the median (B intersection C).
But for P(B|C) the denominator is the number of numbers in the data set that are less than the median (C); for P(C|B) the denominator is the number of numbers in the data set that are odd (B).
It is coincidence that the number of numbers less than the median is the same as the number of odd numbers in the data set.
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To the reader, who asked that I show the work I did to get the answer....
I don't see that there is any place where I did NOT show my work. If you have difficulty following what I did, send another "thank you" message indicating what part(s) you don't understand.
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