Question

A child's game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a
(i)Triangle
(ii)Square

Answer 1

Hint: In this problem, we will first find the total number of articles by adding the number of triangles and number of squares. Next, we will find the probability that the lost piece is a triangle which will be equal to the ratio of number of triangles to total number of articles. We will find the probability that the lost piece is a square which will be equal to ratio of number of squares to total number of articles

Complete step-by-step answer:
There are 8 triangles and 10 squares in the child’s game.
First we will find the total number of articles which is equal to the number of triangles and number of squares.
Therefore,
Total number of articles \[ = 8 + 10 = 18\]
Now, we will find the probability that the lost piece is a triangle which will be equal to the ratio of number of triangles to total number of articles.
Mathematically, we can it as
\[ \Rightarrow P\left( {{\rm{triangle}}} \right) = \] Number of triangles \[ \div \] The total number of articles
Now, substituting the value of number of triangles and the total number of articles in the above equation, we get
\[ \Rightarrow P\left( {{\rm{triangle}}} \right) = \dfrac{8}{{18}}\]
Dividing the numerator and denominator by its common factor, we get
\[ \Rightarrow P\left( {{\rm{triangle}}} \right) = \dfrac{4}{9}\]
Thus, the probability that the lost piece is a triangle is equal to \[\dfrac{4}{9}\].
Now, we will find the probability that the lost piece is a square which will be equal to the ratio of the number of squares to total number of articles.
Mathematically, we can it as
\[ \Rightarrow P\left( {{\rm{square}}} \right) = \] Number of squares \[ \div \] The total number of articles
Now, substituting the value of number of squares and the total number of articles in the above equation, we get
\[ \Rightarrow P\left( {{\rm{square}}} \right) = \dfrac{{{\rm{10}}}}{{{\rm{18}}}}\]
Dividing the numerator and denominator by its common factor, we get
\[ \Rightarrow P\left( {{\rm{square}}} \right) = \dfrac{5}{9}\]
Thus, the probability that the lost piece is a square is equal to \[\dfrac{5}{9}\].
Note: Here the important terms that we need to remember is probability and its properties. Probability is defined as the ratio of number of desired or favorable outcomes to the total number of possible outcomes. In addition to this, the value of probability cannot be greater than 1 and value of probability cannot be negative. Also, the probability of a sure event is always one.