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Probability

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Question : 120 of 127

Marks: +1, -0

Three balls are drawn at random from a bag containing 6 blue and 4 red balls. What is the chance that 2 balls are blue and 1 is red? [MTP-Oct-19]

$\frac{1}{4}$
$\frac{3}{4}$
$\frac{1}{2}$
None of these

Solution:

Concept:

Probability = (favorable outcomes) / (total outcomes).

Explanation:

Total balls =

6 + 4 = 10

.

Total ways to draw 3 balls =

\binom{10}{3} = 120

.

Favorable: choose 2 blue from 6 and 1 red from 4:

\binom{6}{2} \times \binom{4}{1} = 15 \times 4 = 60

.

Probability =

\frac{60}{120} = \frac{1}{2}

.

Answer:

\frac{1}{2}

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