Class 10 maths Probability Hots Questions

Q 11 :

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:

(iii) (a) What is the probability of favourite colour not being red or blue?

(4)

Central angle for favourite colour being red or blue
= central angle for favourite colour being red + central angle for favourite colour being blue

$= 36^{\circ} + 72^{\circ} = 108^{\circ}$

Probability of favourite colour not being red or blue

$= 1 - probability of favourite colour being red or blue = 1 - \frac{A r e a o f r e g i o n o f f a v o u r i t e c o l o u r b e i n g r e d o r b l u e}{A r e a o f c i r c l e} = 1 - \frac{\frac{108 °}{360 °} \times π r^{2}}{π r^{2}} = 1 - \frac{3}{10} = 1 - \frac{\frac{108 °}{360 °} \times π r^{2}}{π r^{2}} = 1 - \frac{3}{10} = \frac{7}{10} = 0.7$

Q 12 :

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:

(iii) (b) What is the probability of favourite colour not being orange or green?

(1)

Central angle for favourite colour being orange or green = central angle for favourite colour being orange + central angle for favourite colour being green

$= 144 ° + 36 ° = 180 °$

Probability of favourite colour not being orange or green

$= 1 - probability of favourite colour being orange or green$

$= 1 - \frac{Area of region of favourite colour being orange or green}{Area of circle}$

$= 1 - \frac{\frac{180 °}{360 °} \times π r^{2}}{π r^{2}}$

$= 1 - \frac{1}{2} = \frac{1}{2}$

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