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What is the probability that an integer x \((1 \leq x \leq 25)\) chosen at rando...


Question

What is the probability that an integer x \((1 \leq x \leq 25)\) chosen at random is divisible by both 2 and 3?

Options

A) \(\frac{1}{25}\)

B) \(\frac{1}{5}\)

C) \(\frac{4}{25}\)

D) \(\frac{3}{4}\)

The correct answer is C.

Explanation:

\((1 \leq x \leq 25)\) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}
Number N of x divisible by both 2 and 3 is 4.
n(\(\varepsilon\)) = 25
= \(\frac{N}{n(\varepsilon)}\)
= \(\frac{4}{25}\)

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Dicussion (1)

  • \((1 \leq x \leq 25)\) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}
    Number N of x divisible by both 2 and 3 is 4.
    n(\(\varepsilon\)) = 25
    = \(\frac{N}{n(\varepsilon)}\)
    = \(\frac{4}{25}\)

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