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 $15?  Options:	A) 5 /16	B) 15/ 32	C) 1/ 2	D) 2/32	E) 11/ 16
After 5 tries Kate to have more than initial sum of 10$ and less than 15$ must win 3 or 4 times (if she wins 2 or less times she'll have less than 10$ and if she wins 5 times she'll have 15$).   So the question becomes "what is the probability of getting 3 or 4 tails in 5 tries?".   P(t=3 or t=4)=P(t=3)+P(t=4)=C35∗(12)5+C45∗(12)5=1532P(t=3 or t=4)=P(t=3)+P(t=4)=C53∗(12)5+C54∗(12)5=1532   Answer: 15/ 32.
<result>B</result>
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?