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# Probability

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What is the probability that a randomly selected integer in the set { 1, 2, 3 ... 100 } is divisible by 2 and not divisible by 8? Express your answer as a common fraction.

Feb 3, 2022

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$$\frac{\mbox{Total number of all possible solutions}}{\mbox{Total number of all solutions}}$$

You can choose 100 numbers so

$$\frac{n}{100}$$ .

There are 50 numbers that are divisible by 2 in the set { 1, 2, 3, ..., 100 }.

In the set { 1, 2, 3, ..., 100 } there are 12 numbers divisible by 8.

Every multiple of 8 is divisible by 2, so (50 - 12 =) 38 possible solutions. (n = 38)

$$\frac{38}{100} = \frac{19}{50} = 0.38 = 38\%$$

Feb 3, 2022