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A Box Contains 10 Red Marbles, 20 Blue Marbles and 30 Green Marbles. 5 Marbles Are Drawn at Random. from the Box, What is the Probability that At Least One is Green?

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Question

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that  at least one is green?

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Solution

Out of 60 marbles, five marbles can be drawn in 60C5 ways.
∴ Total number of elementary events = 60C5

 P (no green) = \[\frac{\text{ Favourable outcomes} }{\text{ Total outcomes } }\]

                       = \[\frac{{}^{30} C_5}{{}^{60} C_5}\]

Thus, P(at least one green) = 1 – P (no green)

\[= 1 - \frac{^{30}{}{C}_5}{^{60}{}{C}_5}\]
\[ = 1 - \frac{117}{4484}\]
\[ = \frac{4484 - 117}{4484}\]
\[ = \frac{4367}{4484}\]

 
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Concept of Probability - Probability of 'Not', 'And' and 'Or' Events
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Chapter 33: Probability - Exercise 33.3 [Page 47]

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R.D. Sharma Mathematics [English] Class 11
Chapter 33 Probability
Exercise 33.3 | Q 36.2 | Page 47

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