csat-suneung 2013 Q8

csat-suneung · South-Korea · csat__math-science 3 marks Conditional Probability Bayes' Theorem with Production/Source Identification
At a certain school, $60 \%$ of all students commute by bus, and the remaining $40 \%$ walk to school. Of the students who commute by bus, $\frac { 1 } { 20 }$ were late, and of the students who walk, $\frac { 1 } { 15 }$ were late. When one student is randomly selected from all students at this school and is found to be late, what is the probability that this student commuted by bus? [3 points]
(1) $\frac { 3 } { 7 }$
(2) $\frac { 9 } { 20 }$
(3) $\frac { 9 } { 19 }$
(4) $\frac { 1 } { 2 }$
(5) $\frac { 9 } { 17 }$
At a certain school, $60 \%$ of all students commute by bus, and the remaining $40 \%$ walk to school. Of the students who commute by bus, $\frac { 1 } { 20 }$ were late, and of the students who walk, $\frac { 1 } { 15 }$ were late. When one student is randomly selected from all students at this school and is found to be late, what is the probability that this student commuted by bus? [3 points]\\
(1) $\frac { 3 } { 7 }$\\
(2) $\frac { 9 } { 20 }$\\
(3) $\frac { 9 } { 19 }$\\
(4) $\frac { 1 } { 2 }$\\
(5) $\frac { 9 } { 17 }$