What is the probability that an integer x,(1 \(\leq\) x \(\leq\) 20) chosen at random is divisible by both 2 and 3?
A
\(\frac{1}{20}\)
B
\(\frac{1}{3}\)
C
\(\frac{3}{20}\)
D
\(\frac{7}{10}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
A = {x/x is divisible by 2}
A = {2,4,6,8,10,12,14,16,18,20}
B = {x/x is divisible by 3}
A ∩ B = {6, 12, 18}
P(Number divisible by both 2 and 3)
= 3/20
Source: Myschool Past Questions Archive (Record #8615)