Two bottles are drawn with replacement from a crate containing 8 Coke, 12 Fanta, and 4 Sprite bottles. What is the probability that the first is coke and the second is not coke?
A
\(\frac{1}{12}\)
B
\(\frac{1}{6}\)
C
\(\frac{2}{9}\)
D
\(\frac{3}{8}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Total = 8 + 12 + 4
= 24
\(\frac{8}{24} \times (\frac{12}{24} + \frac{4}{24}\))
= \(\frac{1}{3} \times (\frac{1}{2} + \frac{1}{6}\))
= \(\frac{1}{3} \times \frac{3 + 1}{6}\)
\(\frac{1}{3} \times \frac{4}{6} = \frac{2}{9}\)
Source: Myschool Past Questions Archive (Record #50132)