If U = {x : x is an integer and 1 \(\leq\) x \(\leq\) 20}...

JAMB 2000

If U = {x : x is an integer and 1 \(\leq\) x \(\leq\) 20}
E\(_1\) = {x : x is a multiple of 3}
E\(_2\) = {x : x is a multiple of 4}
and an integer is picked at random from U, find the probability that it is not in E\(_2\)

A. 3/4
B. 3/10
C. 1/4
D. 1/20

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Correct Answer: Option A

Explanation

U = {1, 2, 3, 4, 5,..., 20}
E1 = {3, 6, 9, 12, 15, 18}
E2 = {4, 8, 12, 16, 20}
P(E\(_2\)) = \(\frac{5}{20}\)
P(not E\(_2\)) = 1 - (\(\frac{5}{20}\)) = \(\frac{15}{20} = \frac{3}{4}\)

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