Answer to Question #330174 in Statistics and Probability for Robera

Question

In a large graduating class of 100 students 54 studied mathematics, 69 studied library science, and 35 studied

both mathematics and library science. If one of these students is selected at random, find the probability that

a) The student takes mathematics or library science

b) The student does not take either of these subjects

c) The student takes library science but not mathematics

Answer 1

$A-math\\B-library\\P\left( A \right) =\frac{54}{100}=0.54\\P\left( B \right) =\frac{69}{100}=0.69\\P\left( A\cap B \right) =\frac{35}{100}=0.35\\a:\\P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A\cap B \right) =0.54+0.69-0.35=0.88\\b:\\P\left( \bar{A}\cap \bar{B} \right) =1-P\left( A\cup B \right) =1-0.88=0.12\\c:\\P\left( \bar{A}\cap B \right) =P\left( B \right) -P\left( A\cap B \right) =0.69-0.35=0.34$