Answer to Question #117293 in Statistics and Probability for Probability

Question

In a school group of 45 students, 37 did the Biology, Physics and 20 Math tasks. a) What is the probability that a student did the Math or Biology assignment? b) What is the probability that he did not do any of the three tasks?

Answer 1

A=biology, $P(A)=37/45$

B=Physics, $P(B)=37/45$

C=Math, $P(C)=20/45$

a) $P(A+C)=P(A)+P(C)-P(AC)= \frac{37}{45}+\frac{20}{45}-\frac{37}{45}\cdot\frac{20}{45}\approx 0.9012$

b) $P(\overline{ABC})=(1-P(A))(1-P(B))(1-P(C))=\frac{8}{45}\cdot \frac{8}{45}\cdot\frac{25}{45}\approx0.0176$