Answer to Question #321071 in Statistics and Probability for Sandy

Question

Bag A contains 10 marbles of which 2 are red and 8 are black. Bag B contains 12 marbles of which 4 are red and 8 are black. A ball is drawn at random from each bag.

a) Draw a probability tree diagram to show all the outcomes the experiment.

b) find the probability that:

i. Both are red

ii. Both are black

iii) one black and one red

iv) at least one red

Answer 1

$i:\\P\left( RR \right) =\frac{2}{10}\cdot \frac{4}{12}=\frac{1}{15}\\ii:\\P\left( BB \right) =\frac{8}{10}\cdot \frac{8}{12}=\frac{8}{15}\\iii:\\P\left( RB\,\,or\,\,BR \right) =\frac{2}{10}\cdot \frac{8}{12}+\frac{8}{10}\cdot \frac{4}{12}=\frac{2}{5}\\iv:\\P\left( at\,\,least\,\,one\,\,R \right) =1-P\left( BB \right) =1-\frac{8}{15}=\frac{7}{15}$