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NDA Math Probability

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Question : 72 of 100

Marks: +1, -0

A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls.If one ball is drawn from each bag,then probability that one ball is white and one ball is black is

$\frac{5}{24}$
$\frac{13}{24}$
$\frac{1}{4}$
$\frac{2}{3}$

Solution:

P (one white ball

\&

one black ball )

P {[black from 1 st bag & white from 2nd] or [white from 1 st & black from 2nd]}

=P([B_1 \cap W_2) \cup (W_1 \cap B_2])

=P(B_1 \cap W_2)+P(W_1 \cap B_2)

(By addition theorem for mutually exclusive events)

=P(B_1)P(W_2)+P(W_1)P(B_2)

(

\therefore B_2

&

W_2;B_2

&

W_1

are pairs of independent events)

=\left[\;\;\frac{2}{6} \times \;\;\frac{3}{8}\right]+\left[\;\;\frac{4}{6} \times \;\;\frac{5}{8}\right]

=\frac{13}{24}

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