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Probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSProbability2 Marks
Question
A bag contains 8 red, 3 white and 9 blue balls. if three balls are drawn at random, determine the probability that:
  1. All the three balls are blue balls
  2. All the balls are of different colours.
✓

Answer

Bag: 8 - Red, 3 - White, 9 - Blue, since three balls are drawn $\therefore\text{n}\text{(s)}=\ ^{20}\text{C}_3$
  1. Let E be the event that all the three balls are blue
$\therefore\text{n}\text{(E)}=\ ^{9}\text{C}_3$
$\therefore\text{P}\text{(s)}=\frac{\ ^{9}\text{C}_3}{\ ^{20}\text{C}_3}$
$=\frac{9\times8\times7}{20\times19\times18}=\frac{7}{95}$
  1. Let E be the event that all the balls are of different colour.
$\therefore\text{n}\text{(s)}=\ ^{8}\text{C}_1\times\ ^{3}\text{C}_1\times\ ^{9}\text{C}_1$
$\therefore\text{p}\text{(E)}=\frac{\ ^{8}\text{C}_1\times\ ^{3}\text{C}_1\times\ ^{9}\text{C}_1}{\ ^{20}\text{C}_3}$
$=\frac{18}{95}$

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