Josh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18? Select the correct option:  A) 1/64  B) 15/64  C) 21/64  D) 21/32  E) 5/6
minimum number of times to win is 4 to have more than 12 apples .   coz: if he wins 3 times =&gt; he gets 3 apples and give 3 apples ; no change   so he needs to win 4 times OR 5 times   Not 6 times because ,   if he wins 6 times =&gt; he gets 6 apples and he will have 18 apples   Now number of ways to win 4 times out of 6 times 621/644   Now number of ways to win 5 times out of 6 times 621/645   Total number of ways 2626 ways   Probability =(621/644) + (621/645)/2^6   =21/64   Answer :21/64
<result>C</result>
Josh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18?