Kate 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 W that Kate has more than $10 but less than $15?
Choose the correct choice from the following answers
A) 5/16  B) 1/2  C) 12/30  D) W=15/32  E) W=3/8
For 21 heads Kate will end up with &lt; $10 and we want her to win. Therefore, only possibilities W are 3 or 4 heads.   I made an educated guess and it worked fine.   Ans- 'D'   MGMAT's anagram helped here as well.   HHHHT = 5!/4!*1! = 5   HHHTT = 5!/3!*2! = 10   Total acceptable cases = 15   Total cases = 32   P = 15/32.W=15/32
<result>D</result>
Kate 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 W that Kate has more than $10 but less than $15?