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14.Probability
medium
A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red
A
$\frac{1}{{10}}$
B
$\frac{1}{{15}}$
C
$\frac{3}{{10}}$
D
$\frac{2}{{21}}$
Solution
(b) We have total number of balls = $10$
$\therefore $ Number of red balls = $3$
and number of black balls = $7$
and number of balls in the bag = $3 + 7 = 10$
$\therefore $The probability for taking out one red ball out of $10$ balls = $\frac{3}{{10}}$ and the probability for taking out one red ball out of remaining $9$ balls = $\frac{2}{9}$
$\therefore $ Probability for both balls to be red
i.e., $p = \frac{3}{{10}} \times \frac{2}{9} = \frac{1}{{15}}$.
Standard 11
Mathematics
