Question

A ball is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. The probability of a ball drawn is red, white or blue:
a) $\dfrac{1}{3}$
b) $\dfrac{3}{5}$
c) $\dfrac{2}{3}$
d) $\dfrac{4}{5}$

Answer 1

Hint:
This question contains different types of balls like 10 red, 30 white, 20 blue and 15 orange and all are put in a box. So, if we draw a ball from the box that contains all types of balls, the one coming out may be white, red, blue or orange, but according to the question, we have to find out the probability of occurring of red, white, blue or orange balls. So, we find out the probability of all the individual color balls like red, white, blue and find out the union of red, white and blue ball probability.

Complete step by step solution:
As the no. of different color balls are given: Red (10), White (30), Blue (20) and Orange (15). Now, we have to calculate the probability of each type of colored balls.
Step 1: Since, the number of red balls is 10, no. of white balls is 30, blue balls is 20 and orange balls is 15. So,
\[\begin{align}
  & \begin{array}{*{35}{l}}
   Total\text{ }no\text{ }of\text{ }sample\text{ }space\text{ }=\text{ }Red\text{ }+\text{ }White\text{ }+\text{ }Blue\text{ }+\text{ }Orange\text{ }balls \\
   =10+30+20+15 \\
\end{array} \\
 & =75\text{ }balls \\
\end{align}\]
Step 2: Now, we are going to calculate the probability of all these balls which is required to find out. So,
\[The\text{ }probability\text{ }of\text{ }1\text{ }red\text{ }ball\text{ }=\text{ }\dfrac{\left( No\text{ }of\text{ }red\text{ }balls \right)}{\left( Total\text{ }no.\text{ }of\text{ }balls \right)}=\text{ }\dfrac{10}{75}\]
\[\therefore The\text{ }probability\text{ }of\text{ }1\text{ }white\text{ }ball\text{ }=\text{ }\dfrac{30}{75}\]
$\therefore The\text{ }probability\text{ }of\text{ }1\text{ }blue\text{ }ball\text{ }=\text{ }\dfrac{20}{75}$
Step 3: Since, according to the question, the probability of finding out any one ball among the colored balls, so we perform union operation.
⸫ Probability of finding out 1 red, white or blue ball is
$\begin{align}
  & =(\dfrac{10}{75}+\dfrac{30}{75}+\dfrac{20}{75}) \\
 & =\dfrac{10+30+20}{75} \\
 & =\dfrac{60}{75} \\
 & =\dfrac{4}{5} \\
\end{align}$

Note:
This question can be solved by a student also from another method, but in this method, a student can understand each and every step directly without much manipulation. Thus, a simple concept of probability is used.