TMUA Official 2022 Paper 1 · Question 19

Official papers

Official 2022 Paper 1 · Q19

Paper 1ProbabilityGeometryFunctions & graphs

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\le a\le2\quad\text{and}\quad-3\le b\le3.

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 $C_1$ ?

\frac1{25}

\frac9{25}

\frac{16}{25}

\frac{6-\pi}6

\frac{16-\pi}{24}

\frac{24-\pi}{24}

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