csat-suneung 2010 Q28b

csat-suneung · South-Korea · csat__math-science 3 marks Conditional Probability Bayes' Theorem with Production/Source Identification
[Probability and Statistics] A training facility has three courses A, B, and C to be experienced in order, with the entrance and exit being the same. There are 30 envelopes at course A, 60 envelopes at course B, and 90 envelopes at course C. Each envelope contains 1, 2, or 3 coupons. The following table shows the number of envelopes by the number of coupons for each course.
\multicolumn{1}{|c|}{Number of Coupons}123Total
A2010030
B30201060
C40302090

After completing each course, a student randomly selects one envelope from that course and receives the coupons inside. A student who started first completed all three courses and received a total of 4 coupons. What is the probability that the student received 2 coupons at course B? [3 points]
(1) $\frac { 6 } { 23 }$
(2) $\frac { 8 } { 23 }$
(3) $\frac { 10 } { 23 }$
(4) $\frac { 12 } { 23 }$
(5) $\frac { 14 } { 23 }$
[Probability and Statistics] A training facility has three courses A, B, and C to be experienced in order, with the entrance and exit being the same. There are 30 envelopes at course A, 60 envelopes at course B, and 90 envelopes at course C. Each envelope contains 1, 2, or 3 coupons. The following table shows the number of envelopes by the number of coupons for each course.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
\multicolumn{1}{|c|}{Number of Coupons} & 1 & 2 & 3 & Total \\
\hline
A & 20 & 10 & 0 & 30 \\
\hline
B & 30 & 20 & 10 & 60 \\
\hline
C & 40 & 30 & 20 & 90 \\
\hline
\end{tabular}
\end{center}

After completing each course, a student randomly selects one envelope from that course and receives the coupons inside. A student who started first completed all three courses and received a total of 4 coupons. What is the probability that the student received 2 coupons at course B? [3 points]\\
(1) $\frac { 6 } { 23 }$\\
(2) $\frac { 8 } { 23 }$\\
(3) $\frac { 10 } { 23 }$\\
(4) $\frac { 12 } { 23 }$\\
(5) $\frac { 14 } { 23 }$