Question 1152413: In a certain college, 25% of boys and 10% of girls are studying mathematics. The girls constitute 60% of the student body. (a) What is the probability that mathematics is being studied? (b) If a student is selected at random and is found to be studying mathematics, find the probability that the student is a girl? (c) a boy?
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
(a) P(Math) = P(Math,girls) + P(Math,boys) = 0.6*0.1 + 0.4*0.25 = 0.16. ANSWER
(b) P(girl) = P(Math,girls) / P(Math) =  =  = 0.375. ANSWER
(c) P(boy) = P(Math,boys) / P(Math) =  =  = 0.625. ANSWER
Notice that 0.375 + 0.625 = 1, which gives an appropriate test to validity of my answers (b) and (c) . . .
Solved.
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This problem, in its parts (b) and (c), is on Conditional probability.
On conditional probability, see the lesson
- Conditional probability problems
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Solved problems on Probability".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
Consider these lessons as your textbook, handbook, a Solutions Manual, tutorials and (free of charge) home teacher.
Happy learning (!)
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