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One urn contains two black balls (labelled $B_1$ and $B_2$ ) and one while ball. A second urn contains one black ball and two white balls (labelled $\mathrm{W}_1$ and $\mathrm{W}_2$ ). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball.
(a) Write the sample space showing all possible outcomes.
(b) What is the probability that two black balls are chosen?
(c) What is the probability that two balls of opposite colour are chosen?
(a) Write the sample space showing all possible outcomes.
(b) What is the probability that two black balls are chosen?
(c) What is the probability that two balls of opposite colour are chosen?
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(a) Sample sapce $=\left\{B_1 B_2, B_1 W, B_2 W, B_2 B_1\right.$, $\left.\mathrm{WB}_1, \mathrm{WB}_2, \mathrm{BW}_1, \mathrm{BW}_2, \mathrm{~W}_1 \mathrm{~B} . \mathrm{W}_2 \mathrm{~B}, \mathrm{~W}_1 \mathrm{~W}_2, \mathrm{~W}_2 \mathrm{~W}_1\right\}$
(b) $\mathrm{P}(2$ Black Balls $)=\frac{2}{12}=\frac{1}{6}$
(c) $\mathrm{P}(2$ balls of opposite colour $)=\frac{8}{12}=\frac{2}{3}$
(b) $\mathrm{P}(2$ Black Balls $)=\frac{2}{12}=\frac{1}{6}$
(c) $\mathrm{P}(2$ balls of opposite colour $)=\frac{8}{12}=\frac{2}{3}$
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