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Probability

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Question : 47 of 127

Marks: +1, -0

Two balls are drawn from a bag containing 5 white and 7 black balls at random. What is the probability that they would be of different colours?

$\frac{35}{66}$
$\frac{30}{66}$
$\frac{12}{66}$
None

Solution:

Concept:

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

Explanation:

Total balls = 5 white + 7 black = 12.

Total ways to choose 2 balls =

\binom{12}{2} = 66

.

Favorable: one white and one black.

Ways to choose 1 white from 5 =

\binom{5}{1} = 5

.

Ways to choose 1 black from 7 =

\binom{7}{1} = 7

.

Total favorable ways =

5 \times 7 = 35

.

Probability =

\frac{35}{66}

.

Answer:

\frac{35}{66}

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