question_answer

A bag contains white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is \[\frac{3}{10}\] and that of a black ball is \[\frac{2}{5}\] then find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

Answer:

Given, the probability of getting a white ball

\[\Rightarrow P(W)=\frac{3}{10}\]

and the probability of getting a black ball

\[\Rightarrow P(B)=\frac{2}{5}\]

then, the probability of getting a red ball

\[\Rightarrow P(R)=1-\frac{3}{10}-\frac{2}{5}=\frac{10-3-4}{10}=\frac{3}{10}\]

Now, \[\frac{2}{5}\] of total number of balls \[=20\]

Total number of balls \[=\frac{20\times 5}{2}\]

\[=50\]

Hence, the total no. of balls in the bag is \[50\].