A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour?

Created: 5 months ago | Updated: 1 week ago

Job Solution BASIC Bank Ltd Basic Bank Ltd. || Assistant Manager (16-03-2018) || 2018 গণিত

138

প্রশ্নে বলা হচ্ছে, একটি বক্সে 5 টি সবুজ, 4 টি হলুদ এবং 3 টি সাদা বল রয়েছে। তাদের মধ্য হতে 3 টি বল দৈবভাবে উত্তোলন করা হলো। ঐ 3 টি বল-ই এক রঙের না হবার সম্ভাব্যতা কত?

Number of green ball = 5

∴ Number of yellow ball = 4

∴ Number of white ball = 3

∴ Total ball=5+4+3=12

P(Being 3 same colour) = P(3 green) + P(3 yellow) + P (3 white)

$= \frac{5 c_{3}}{12 c_{3}} + \frac{4 c_{3}}{12 c_{3}} + \frac{3 c_{3}}{12 c_{3}} = \frac{10}{220} + \frac{4}{220} + \frac{1}{220} = \frac{10 + 4 + 1}{220} = \frac{15}{220} = \frac{3}{44}$

∴ P(Being 3 not same colour) $= 1 - \frac{3}{44} = \frac{44 - 3}{44} = \frac{41}{44}$

$A n s w e r : T h e p r o b a b i l i t y o f n o t b e i n g 3 s a m e c o l o u r i s \frac{41}{44}$

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A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour?

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