A bag contains 4 red, 6 blue and 8 green identical marbles. (a) If three marbles are drawn at random, without replacement, calculate the probability that : ...
Question 1 Report
A bag contains 4 red, 6 blue and 8 green identical marbles.
(a) If three marbles are drawn at random, without replacement, calculate the probability that :
(i) all will be green ; (ii) all will have the same colour.
(b) If each marble is replaced before another is drawn, calculate the probability that all will have the same colour.
Answer Details
Total marbles \(=4R+6B+8G=18\).
(a) Without replacement.
(i) all green:
\[\frac{8}{18}\cdot\frac{7}{17}\cdot\frac{6}{16}=\frac{336}{4896}=\frac{7}{102}\approx 0.069.\](ii) all the same colour = all red + all blue + all green:
\[\frac{4}{18}\cdot\frac{3}{17}\cdot\frac{2}{16}+\frac{6}{18}\cdot\frac{5}{17}\cdot\frac{4}{16}+\frac{8}{18}\cdot\frac{7}{17}\cdot\frac{6}{16}=\frac{24+120+336}{4896}=\frac{480}{4896}=\frac{5}{51}\approx 0.098.\](b) With replacement (each draw from all 18):
\[\left(\frac{4}{18}\right)^3+\left(\frac{6}{18}\right)^3+\left(\frac{8}{18}\right)^3=\left(\frac{2}{9}\right)^3+\left(\frac13\right)^3+\left(\frac49\right)^3=\frac{8+27+64}{729}=\frac{99}{729}=\frac{11}{81}\approx 0.136.\]Download The App On Google Playstore
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