Core stretch Assume the landing point is uniformly distributed over the whole board. A circular boar

Question

Core stretch

Assume the landing point is uniformly distributed over the whole board.

A circular board has sectors A, B, C and D with angles $80^\circ,40^\circ,100^\circ,140^\circ$. They score 5, 8, 2 and 1 points, respectively. A dart lands randomly on the board. Find the probability of scoring

8 points,[1]
less than 5 points,[1]
6 points.[1]

Accepted Answer

(i) $\frac{1}{9}$ (ii) $\frac{2}{3}$ (iii) $0$.

Scores on unequal circular sectors

Scores on unequal circular sectors

Solution:

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