SOLUTION: All students at the Academy of Music and Math take both music and math. The probability that a student has an A in math is 1/6. The probability that a student has an A in music is

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Question 188968: All students at the Academy of Music and Math take both music and math. The probability that a student has an A in math is 1/6. The probability that a student has an A in music is 5/12. The probability that a student with an A in math has an a in music plus the probability that a student with an A in music has an a in math is 7/10.
What is the probability that a student has A’s in both subjects?

Answer by Mathtut(3670) (Show Source):
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P(ma and mu)/p(mu)+P(ma and mu)/p(ma)=7/10
:
P(ma and mu)/(5/12)+P(ma and mu)/(1/6)=7/10
:
12*P(ma and mu)/5 + 6*P(ma and mu)=7/10
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12*P(ma and mu)/5 +30 *P(ma and mu)=7/10
:
42*P(ma and mu)=35/10
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P(ma and mu)=35/420=.0833= 1/12
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or just p(ma and mu)=1/6*5/12=5/60=1/12