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Question: A child’s game has 8 triangles of which 3 are blue and rest are red and 10 squares of which 6 are bl...

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
(iii). Square of blue color
(iv). Triangle of red color

Explanation

Solution

Hint: In this problem, first find the total number of articles. Next, find the individual probability by dividing the favorable outcome by total number of articles.

Complete step by step solution:
Total number of articles n(s)=10+8=18n\left( s \right) = 10 + 8 = 18.
The total number of blue triangles is 3.
The total number of red triangles is 5.
The total number of blue squares is 6.
The total number of red squares is 4.
(i) The probability that lost piece is a triangle is calculated as follows:

      P(triangle) = Number of trianglenumber of articles ⇒P(triangle) = 818 ⇒P(triangle) = 49  \,\,\,\,\,\,P\left( {{\text{triangle}}} \right){\text{ = }}\dfrac{{{\text{Number of triangle}}}}{{{\text{number of articles}}}} \\\ \Rightarrow P\left( {{\text{triangle}}} \right){\text{ = }}\dfrac{{\text{8}}}{{{\text{18}}}} \\\ \Rightarrow P\left( {{\text{triangle}}} \right){\text{ = }}\dfrac{4}{9} \\\

(ii) The probability that lost piece is a square is calculated as follows:

      P(square) = Number of squarenumber of articles ⇒P(square) = 1018 ⇒P(square) = 59  \,\,\,\,\,\,P\left( {{\text{square}}} \right){\text{ = }}\dfrac{{{\text{Number of square}}}}{{{\text{number of articles}}}} \\\ \Rightarrow P\left( {{\text{square}}} \right){\text{ = }}\dfrac{{10}}{{{\text{18}}}} \\\ \Rightarrow P\left( {{\text{square}}} \right){\text{ = }}\dfrac{5}{9} \\\

(iii) The probability that lost piece is a square of blue color is calculated as follows:

      P(blue square) = Number of blue squarenumber of articles ⇒P(blue square) = 618 ⇒P(blue square) = 13  \,\,\,\,\,\,P\left( {{\text{blue square}}} \right){\text{ = }}\dfrac{{{\text{Number of blue square}}}}{{{\text{number of articles}}}} \\\ \Rightarrow P\left( {{\text{blue square}}} \right){\text{ = }}\dfrac{6}{{{\text{18}}}} \\\ \Rightarrow P\left( {{\text{blue square}}} \right){\text{ = }}\dfrac{1}{3} \\\

(iv) The probability that lost piece is a triangle of red color is calculated as follows:

      P(red triangle) = Number of red trianglenumber of articles ⇒P(red triangle) = 518  \,\,\,\,\,\,P\left( {{\text{red triangle}}} \right){\text{ = }}\dfrac{{{\text{Number of red triangle}}}}{{{\text{number of articles}}}} \\\ \Rightarrow P\left( {{\text{red triangle}}} \right){\text{ = }}\dfrac{5}{{{\text{18}}}} \\\

Note: Probability of an event is a ratio of favorable outcome to the sample size. To obtain the probability, divide the number of events by the number of possible outcomes. The sum of the possibilities of all the possible outcomes will be 1.