First slide

Theorems of probability

Question

A point is selected at random from the interior of a circle. The probability that the point is closer to the centre than the boundary of the circle is

Moderate

A

$\frac{3}{4}$
B

$\frac{1}{2}$
C

$\frac{1}{4}$
D

$\frac{1}{3}$

Solution

Radius of the circle $= r \Rightarrow n (S) = π r^{2}$
$n (E) = π {(\frac{r}{2})}^{2} = \frac{π r^{2}}{4}$

$P (E) = \frac{\frac{π r^{2}}{4}}{π r^{2}} = \frac{1}{4}$

The probability that the point is closer to the centre than the boundary of the circle is $\frac{1}{4}$

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