A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5

1.	A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that(i) all will be blue? (ii) atleast one will be green?
Answer» Total number of marbles = 10 + 20 + 30 = 60 Number of ways of drawing 5 marbles from 60 marbles = ⁶⁰C₅ (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 ²⁰C₅ ways. ∴ Probability that all marbles will be blue =²⁰C_{5 / ⁶⁰}C₅ (ii) Number of ways in which the drawn marble is not green =^(20+10)C₅ ∴ Probability that no marble is green = ^30C₅ / ⁶⁰C₅ Probability that at least one marble is green = 1 – (^30_C_{5 /}⁶⁰C₅)

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that(i) all will be blue? (ii) atleast one will be green?

Answer»

Total number of marbles = 10 + 20 + 30 = 60
Number of ways of drawing 5 marbles from 60 marbles = ⁶⁰C₅

(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 ²⁰C₅ ways.
∴ Probability that all marbles will be blue =²⁰C_{5 / ⁶⁰}C₅

(ii) Number of ways in which the drawn marble is not green =^(20+10)C₅

∴ Probability that no marble is green = ^30C₅ / ⁶⁰C₅
Probability that at least one marble is green = 1 – (^30_C_{5 /}⁶⁰C₅)

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