Kate and David each have $\$10.$ Together they flip a coin $5$ times. Every time the coin lands on heads, Kate gives

Kate and David each have $\$10.$ Together they flip a coin $5$ times. Every time the coin lands on heads, Kate gives David $\$1.$ Every time the coin lands on tails, David gives Kate $\$1.$ After the coin is flipped $5$ times, what is the probability that Kate has more than $\$10$ but less than $\$15?$

A. $\dfrac5{16}$

B. $\dfrac{15}{32}$

C. $\dfrac12$

D. $\dfrac{21}{32}$

E. $\dfrac{11}{16}$

Answer: B

Source: GMAT Club Tests

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