Question

Some students were asked to list their favourite colour. The measure of each colour is shown by the central angle of the given pie chart. Study the pie chart and answer the following questions.

1. If a student is chosen at random then find the probability of his/her favourite colour being white.
2. What is the probability of his/her favourite colour being blue or green?
3. What is the probability of the favourite colour being red or blue?
4. If 15 students liked the colour yellow, how many students participated in the survey?

Answer 1

Given Data:

Total angle of the circle in the pie chart: \[360^\circ\]

Central angles for colours:

White = \[120^\circ\]

Blue = \[60^\circ\]

Green = \[60^\circ\]

Red = \[30^\circ\]

Yellow = \[90^\circ\]

i. Probability that favourite colour is white:

Formula: \[P(\text{White}) = \frac{\text{Central angle of White}}{\text{Total central angle}}\]

Calculation: \[P(\text{White}) = \frac{120^\circ}{360^\circ} = \frac{1}{3}\]

ii. Probability that favourite colour is blue or green:

Sum of central angles for Blue and Green: \[60^\circ + 60^\circ = 120^\circ\]

Formula and Calculation: \[P(\text{Blue or Green}) = \frac{120^\circ}{360^\circ} = \frac{1}{3}\]

iii. Probability that favourite colour is red or blue:

Sum of central angles for Red and Blue: \[30^\circ + 60^\circ = 90^\circ\]

Formula and Calculation: \[P(\text{Red or Blue}) = \frac{90^\circ}{360^\circ} = \frac{1}{4}\]

iv. Total number of participating students:

Let the total number of students who participated in the survey be x.

Angle representing yellow = \[90^\circ\]

Proportion liking yellow: \[\frac{90^\circ}{360^\circ} = \frac{1}{4}\]

Equation: \[\frac{15}{x} = \frac{1}{4}\]

Solving for x: \[x = 15 \times 4 = 60\]

Conclusion: The total number of students who participated in the survey is 60.