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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability5 Marks
Question
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that,
  1. Both balls are red,
  2. First ball is black and second is red,
  3. One of them is black and other is red.
✓

Answer

The Box contains 10 black balls and 8 red balls.
Then $\text{P(Black ball)}=\frac{10}{18}$
$\text{P(red ball)}=\frac{8}{18}$
  1. P(Both ballls are red) $=\frac{8}{18}\times\frac{8}{18}=\frac{16}{81}$
  2. P (First ball is black and second is red) $=\frac{10}{18}\times\frac{8}{18}=\frac{20}{81}$
  3. P (One of them is black and other is red)
$=\frac{10}{18}\times\frac{8}{18}+\frac{8}{18}\times\frac{10}{18}$

$=2\Big(\frac{20}{81}\Big)$

$=\frac{40}{81}$

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