What is the probability that a number chosen at random from the intergers between 1 and 10 inclusive is either a prime or a multiple of 3?
A
\(\frac{7}{10}\)
B
\(\frac{3}{5}\)
C
\(\frac{4}{5}\)
D
\(\frac{3}{10}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Simple Space: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 10)
Prime: (2, 3, 5, 7)
multiples of 3: (3, 6, 9)
Using: ∣A∪B ∣= ∣A∣ + ∣B∣ − ∣A∩B∣ = 4 + 3 − 1 =6.
Or
Prime or multiples of 3: (2, 3, 5, 6, 7, 9 = 6)
Probability = \(\frac{6}{10}\)
= \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #32265)