Mango Shooters

Probability Level 3

A boy was hungry. He decided to eat mangoes from a tree by shooting at them with a catapult and stones, and making them fall down.

The probability of the boy hitting the mango is $\dfrac {3}{4}$ . How many minimum attempts must he shoot so that probability of hitting the mango at least once is more than 0.99 ?

Not possible 4 10 8 2

2 solutions

Henry U
Feb 8, 2019

For each shot, the probability of not hitting a mango is $1 - \frac 34 = \frac 14$ . The probability of not hitting a mango after $n$ shots is therefore $\left( \frac 14 \right) ^n = \frac 1{4^n}$ .

This has to be less than $0.01$ , so

$\begin{aligned} \frac 1{4^n} &< \frac 1{100} \\ 4^n &> 100 \\ n &> \log_4 100 \approx 3.3 \end{aligned}$

Since $n$ has to be an integer, the smallest possible value is $\boxed 4$ .

Kyle T
Feb 11, 2019

https://www.wolframalpha.com/input/?i=1+-+0.25%5En+%3E+0.99,+n+is+an+integer

Mango Shooters

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