Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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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 All Are Blue? - Mathematics

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 all are blue?

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Solution

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

Out of 20 blue marbles, five blue marbles can be chosen in 20C5 ways.
∴ Favourable number of events = 20C5 ways
Hence, the required probability is given by

\[\frac{^{20}{}{C}_5}{^{60}{}{C}_5} = \frac{20 \times 19 \times 18 \times 17 \times 16}{60 \times 59 \times 58 \times 57 \times 56}\]

\[ = \frac{19 \times 6 \times 17}{59 \times 29 \times 57 \times 7}\]

\[ = \frac{2 \times 17}{59 \times 29 \times 7}\]

\[ = \frac{34}{11977}\] 

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 36.1 | Page 47
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