Given data : 24 gum balls - 12 white and 12 black
3 black gum balls have already been chosen

To find : Probability that next 2 gum balls are also black in color

Denominator(2 gum balls chosen from 21 remaining balls) \(21c2 = \frac{21*20}{2} = 210\)
Numerator(Balls picked are black) \(9c2 = \frac{9*8}{2} = 36\)

Probability that next 2 gum balls are also black in color(of remaining 9 black gum balls) = \(\frac{36}{210} = \frac{6}{35}\)(Option A)
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First three gumballs dispensed were black. That info yields two changes:

1. The total number of gumballs decreases from 24 to 21; and

2. The number of black gumballs decreases from 12 to 9

What is the probability that the next two gumballs dispensed will be black?

First dispensation, probability is \(\frac{9}{21}\).That leaves 8 black and 20 total gumballs.

Second dispensation: probability is \(\frac{8}{20}\)

\(\frac{9}{21}\) * \(\frac{8}{20}\) =

\(\frac{3}{7}\) * \(\frac{2}{5}\) = \(\frac{6}{35}\)

Answer A
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\(\frac{9}{21} * \frac{8}{20} = \frac{3}{7} * \frac{2}{5} = \frac{6}{35}\). Ans - A.
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