Question 113276This question is from textbook
: In a group of 100 students, 30 are HIstory majors, 6 of the History majors have a dual major in Business, in addition there are 45 Business majors, and there are 25 Engineering majors (none of which have dual majors and no student has a triple major. Many students have not declared a major. Determine the probability that a a student selected at random is either a business or engineering major.
***I am confused because I have a total of 100 students and some how I am coming up with a 51% probability that a random student selected is eiher business or engineering; however, I am not taking into consideration those who are NOT declared majors. How far off am I?
This question is from textbook
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! This is a relatively straight-forward counting problem, but you have to be careful not to count someone twice.
First thing is that there are 30 History majors, but 6 of them are dual History/Business majors, that means that there are only 30 - 6 = 24 students that are ONLY History majors. Likewise, of the 45 Business majors, 6 of them are dual, so 45 - 6 = 39 are ONLY Business.
In summary:
24 Only History
39 Only Business
6 History/Business
25 Engineering
All of that totals to 94, but there are 100 students, so that means 6 students have no major at all.
The business majors in the random selection could be either from the Business only group or the dual History/Business group, so that is a total of 45, plus there are 25 Engineering majors, making a total of 70 possibilities out of the 100 students. Therefore the desired probability is 0.70.
As an aid to having this make sense, consider this: The only way a student from this group could NOT be either an Engineering or Business major is if the student were a History ONLY major or had not selected his major yet. There are 24 History only and 6 no major students for a total of 30, so there is a 0.30 probability that the student is NOT either Engineering or Business, or 1 - the probability that the student is from either of those two groups.
Hope this helps
John
|
|
|
