Probability 2

Probability Level 3

An integer $n$ is selected at random from the set of values $100 - 300$ (both inclusive) such that $n = 11 \bmod{17}$ .

If the probability of selection of such a number $n$ is $\frac{a}{b}$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .

The answer is 71.

1 solution

Guillermo Templado
Dec 24, 2016

Relevant wiki: Probability by outcomes-section 2

There are $201$ numbers between 100 and 300 (both inclusive), and 12 $n$ 's satisfying the requisites: $113, 130,... , 300= 113 + 11\times17$ , $113$ is the first number between 100 and 300 such that $113 \equiv 11 \bmod{17}$ because $113 - 11 = 102 = 6 \cdot 17$ . Hence, probability is $\frac{12}{201} = \frac{4}{67} = \frac{a}{b} \Rightarrow a + b = 71$

Probability 2

The answer is 71.

1 solution

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