Question

Find the chance of drawing $2$ blue balls in succession from a bag containing $5$ red and $7$ blue balls, if the balls are not being replaced.

• A. $\frac{21}{64}$
• B. $\frac{7}{22}$
• C. $\frac{21}{66}$
• D. $\frac{3}{13}$

Answer 1

The correct option is B

$\frac{7}{22}$

Find the probability of drawing $2$ blue ball in succession without replacement.

Total number of Red Ball $=5$

Total number of Blue Ball $=7$

Therefore, total number of Ball $=12$

Probability of drawing one Blue Ball in first chance is $=\frac{7}{12}$

Total number of Red Ball $=5$

Total number of Blue Ball $=6$

Now total number of Ball left is $=11$

Probability of drawing another Blue Ball is $=\frac{6}{11}$

Therefore, chance of drawing $2$ blue balls in succession from a bag containing $5$ red and $7$ blue balls, if the balls are not being replaced.is $=\frac{7}{12}\times \frac{6}{11}=\frac{7}{22}$

Hence, the correct option is B.