Darts on a dartboard!

Probability Level 3

After throwing a dart $n$ times at a dartboard, my percentage of hits is $p$ %. With my next throw I make a hit and my percentage is $(p + 1)$ %. Find the value of $n + p$ .

100 89 99 50 49 51 75 20

1 solution

Rui-Xian Siew
Nov 5, 2017

After $n$ throws, the total hits are $\frac{np}{100}$ . After $n+1$ throws, the total hits are $\frac{np}{100} +1$ . Hence,

$\frac{\frac{np}{100} +1}{n+1}=\frac{p+1}{100} \\ np+100=np+n+p+1 \\ \therefore n+p=99$

Darts on a dartboard!

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