Two bottles are drawn with replacement from a crate containing 8 coke, 12 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: Option C
Explanation
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})