TMUA 2022 Paper 1 Q19 — Worked Solution

P1·Statistics & Probability, Coordinate Geometry·7.0Official · 2022 · Q19

geometric-probabilitycircle-intersectionarea-ratio

Circle

C_{1}

is defined as

x^{2} + y^{2} = 25

.A second circle

C_{2}

has radius

4

and centre

(a, b)

where

- 2 \leq a \leq 2 and - 3 \leq b \leq 3.

If the centre of

C_{2}

is equally likely to be located anywhere within the given range, what is the probability that

C_{2}

intersects

C_{1}

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