Question

In a bag there are $6$ red, $4$ black balls. From it $2$ balls (without replacement) are drawn. If the first drawn ball is known to be red, the probability for the second drawn ball is also red is

• A. $\frac{5}{9}$
• B. $\frac{5}{18}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{5}{9}$

Total of no. of balls in a bag $=10$

$\Rightarrow$ No. of red balls $=6,$ No. of black $=4$

$\Rightarrow$ Probability of getting one red ball $=\frac{{}^6{C}_1}{{}^{10}{C}_1}=\frac{6}{10}$

$\Rightarrow$ Probability of drawing a red ball second time $=\frac{{}^5{C}_1}{{}^9{C}_1}=\frac{5}{9}$

Hence, the answer is $\frac{5}{9}.$