Question

A bag contains 10 white, 5 black, 3 green and 2 red balls. One ball is drawn at random. Find the probability that the ball drawn is white or black or green.

Answer 1

HINT: In the question, ‘or’ is used at the end which means that the different probabilities of the different balls are to be added with each other in order to get to the final answer.

Complete step-by-step solution -
The formula for evaluating probability of any event is
P \[=\dfrac{Favorable\ outcomes}{Total\ outcomes}\] .
Another important thing which is useful for this question is that drawing a ball from the bag at random is nothing but taking out a ball without having any bias towards any ball and without having any prior information regarding the balls other than their color.

Now, in the question it is mentioned that there are 10 white balls, 5 black balls, 3 green balls and 2 red balls in the bag.
So, the total outcomes for the event of drawing balls at random from the bag is
Total outcomes \[=10+5+3+2\]
Total outcomes \[=20\] .
Now, for favorable outcomes for getting a white ball, we need to count the total number of white balls which is given as 10 in the question.
Therefore,
Favorable outcomes \[=10\] .
Now, using the formula for calculating the probability of getting a white ball from the bag \[\begin{align}
  & =\dfrac{Favorable\ outcomes}{Total\ outcomes} \\
 & =\dfrac{10}{20} \\
 & =\dfrac{1}{2} \\
\end{align}\]
Hence, the probability of getting a white ball from the bag is \[\dfrac{1}{2}\] .
Similarly, for finding the probability of getting a black ball from the bag, the favorable outcomes are
\[=5\].
 Now, using the formula for calculating the probability of getting a black ball from the bag \[\begin{align}
  & =\dfrac{Favorable\ outcomes}{Total\ outcomes} \\
 & =\dfrac{5}{20} \\
 & =\dfrac{1}{4} \\
\end{align}\]
Similarly, again for finding the probability of getting a red ball from the bag, the favorable outcomes are
\[=3\].
 Now, using the formula for calculating the probability of getting a green ball from the bag \[\begin{align}
  & =\dfrac{Favorable\ outcomes}{Total\ outcomes} \\
 & =\dfrac{3}{20} \\
 & =\dfrac{3}{20} \\
\end{align}\]
Now, the probability of getting a white or a black or a green ball from the bag is calculated as follows
Final probability is
\[\begin{align}
  & =\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{20} \\
 & =\dfrac{10+5+3}{20} \\
 & =\dfrac{18}{20} \\
 & =\dfrac{9}{10} \\
\end{align}\]
  Hence, the probability is \[\dfrac{9}{10}\] .

NOTE: - Another way of doing this question is that as the only probability of a red ball is not asked, so, we can subtract the probability (of getting a red ball from the bag) from 1 and through this method, we will also get the correct answer.