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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.
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Answer

Given: A box containing 10 black and 8 red balls.
Total number of balls in box = 18
Probability of getting a black ball in first draw = $\frac{10}{18}=\frac{5}{9}$
As the ball is replaced after first throw,
Hence, Probability of getting a red ball in second draw = $\frac{8}{18}=\frac{4}{9}$
Now, Probability of getting first ball is black and second is red = $\frac{5}{9} \times \frac{4}{9}=\frac{20}{81}$
Probability of getting a red ball in first draw = $\frac{8}{18}=\frac{4}{9}$
As the ball is replaced after first throw,
Hence, Probability of getting a black ball in second draw = $\frac{10}{18}=\frac{5}{9}$
Now, Probability of getting first ball is red and second is black = $\frac{4}{9} \times \frac{5}{9}=\frac{20}{81}$
Therefore, Probability of getting one of them is black and other is red :
= Probability of getting first ball is black and second is red + Probability of getting first ball is red and second is black
= $\frac{20}{81}+\frac{20}{81}$ = $\frac{40}{81}$

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