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Start the planKate and Danny each have \(\$10.\) Together, they flip a fair coin \(5\) times. Every time the coin lands on heads, Kate gives Danny \(\$1.\) Every time the coin lands on tails, Danny gives Kate \(\$1.\) After the five-coin flips, what is the probability that Kate has more than \(\$10\) but less than \(\$15?\)
(A) \(\dfrac5{16}\)
(B) \(\dfrac12\)
(C) \(\dfrac{12}{30}\)
(D) \(\dfrac{15}{32}\)
(E) \(\dfrac38\)
Answer: D
Source: Manhattan GMAT
(A) \(\dfrac5{16}\)
(B) \(\dfrac12\)
(C) \(\dfrac{12}{30}\)
(D) \(\dfrac{15}{32}\)
(E) \(\dfrac38\)
Answer: D
Source: Manhattan GMAT
