csat-suneung 2012 Q13

csat-suneung · South-Korea · csat__math-science 3 marks Probability Definitions Conditional Probability and Bayes' Theorem
Box A contains 3 red balls and 5 black balls, and box B is empty. When 2 balls are randomly drawn from box A, if a red ball appears, perform [Execution 1], and if no red ball appears, perform [Execution 2]. What is the probability that the number of red balls in box B is 1? [3 points] [Execution 1] Put the drawn balls into box B. [Execution 2] Put the drawn balls into box B, and then randomly draw 2 more balls from box A and put them into box B.
(1) $\frac { 1 } { 2 }$
(2) $\frac { 7 } { 12 }$
(3) $\frac { 2 } { 3 }$
(4) $\frac { 3 } { 4 }$
(5) $\frac { 5 } { 6 }$
Box A contains 3 red balls and 5 black balls, and box B is empty. When 2 balls are randomly drawn from box A, if a red ball appears, perform [Execution 1], and if no red ball appears, perform [Execution 2]. What is the probability that the number of red balls in box B is 1? [3 points]\\

[Execution 1] Put the drawn balls into box B.\\

[Execution 2] Put the drawn balls into box B, and then randomly draw 2 more balls from box A and put them into box B.\\
(1) $\frac { 1 } { 2 }$\\
(2) $\frac { 7 } { 12 }$\\
(3) $\frac { 2 } { 3 }$\\
(4) $\frac { 3 } { 4 }$\\
(5) $\frac { 5 } { 6 }$