# Physics

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A class has 50 students. 13 are juniors, 20 are psych majors, and 24 are neither psych majors nor juniors. How many psych majors are juniors?

• Probability -

My drawing shows that

Note:
Pr(Junior or Psy)= Pr(Jun)+ Pr(Psy)-Pr(Junior AND Psy)

But you are given Pr (NOT(Junior Or Psy), so Pr(Junior or Psy)=1-Pr( Not(junior or Psy).

Finally, then
Pr(Junior ANd Psy)=Pr(Jun)+Pr(Psy)-Pr(Jun or Psy)
= Pr(Jun)+ Pr(Psy)-(1-Pr(NOT(Jun or Psy))
= 13/50 + 20/50-1+24/50
=57/50-1= 7/50
so 7 Psy majors are Juniors.

check my thinking.

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