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.

\(\frac{3}{8}\)

Correct answer is C

Total = 8 + 12 + 4

= 24

\(\frac{8}{24} \times (\frac{12}{24} + \frac{4}{24}\))

= \(\frac{1}{3} \times (\frac{1}{2} + \frac{1}{6}\))

= \(\frac{1}{3} \times \frac{3 + 1}{6}\)

\(\frac{1}{3} \times \frac{4}{6} = \frac{2}{9}\)

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