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Solution


Q.

A survey was conducted at a high school, and the results were displayed in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response.

Based on the above information, answer the following questions:

 

(i) What is the probability of favourite colour being red
1 0.1  
2 0.2  
3 0.4  
4 0.3  

Ans.

(1)

We know that the area of the sector of a circle is θ360°×πr2, where r is the radius and θ is the angle (central angle) of sector.  Let the radius of circular graph be r units.

(i) Central angle for favourite colour being red =  36∘

Probability of favourite colour being red =Area of region of favourite colour being redArea of circle

=36°360°×πr2πr2

=110=0.1