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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 - (\(\frac{5}{20}\)) = \(\frac{15}{20} = \frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #1077)