10th Class Mathematics Probability Question Bank MCQs - Probability

A bag contains 8 red balls and some blue balls. If the probability of drawing a blue ball is three times of a red ball, then the number of blue balls in the bag:

A) 12

B) 18

C) 24

D) 36

Correct Answer: C

Solution :

[c] Let there be x blue balls in the bag.

Hence, total number of balls in the bag

\[=(8+x)\]and Now, \[{{p}_{1}}\] = Probability of drawing a blue ball

\[=\frac{x}{8+x}\]

and \[{{p}_{2}}=\] Probability of drawing a red ball

\[=\frac{8}{8+x}\]

It is given that, \[{{p}_{1}}=3{{p}_{2}}\]

\[\frac{3}{8+x}=3\times \frac{8}{(8+x)}\]

\[\frac{3}{8+x}=\frac{24}{8+x}\]

\[x=24.\]

Hence, there are 24 blue balls in the bag.