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 that Kate has more than $10 but less than $15? Choose the correct choice from the following options:	A) 5/16	B) 1/2	C) 12/30	D) 15/32	E) 3/8
the probability of the coin landing tails up either 3 or 4 times = P(3t) + P(4t)   Binomial distribution formula: nCk p^k (1-p)^(n-k)   P(3t) = 5C3 (1/2)^3 (1/2)^2 = 10 (1/2)^5   P(4t) = 5C4 (1/2)^4 (1/2)^1 = 5 (1/2)^5   =&gt; P(3t) + P(4t) = 15/32   Answer: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 that Kate has more than $10 but less than $15?