A box contains 10 rd marbles, 20 blue marbles and 30 green marbles. Five marbles are drawn from the box, what is the probability that i. al will be blue? ii. at least one will be green?

Explanation

Total number of marbles =10+20+30=60

Number of ways of drawing 5 marbles from 60 marbles `=^60C_5`
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(i) All the drawn marbles will be blue if we draw 5 marbles out of 20 blue marbles

5 blue marbles can be drawn from 20 blue marbles in `.^20C_5`​ ways

∴ Probability that all marbles will be blue =`​(^20C_5)/(^60C_5)`
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(ii) Number of ways in which the drawn marble is not green =`^(20+10)C_5​=^30C_5`
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⇒ Probability that no marble is green =`(.^​30C_5)/(^60C_5)`
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∴ Probability that at least one marble is green =`1−(.^​30C_5)/(^60C_5)`