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May 4th, 2018, 02:12 AM  #1 
Senior Member Joined: Jul 2011 Posts: 400 Thanks: 15  probability problem
a Dice is thriwn $31$ times. Then probability of getting $2,4$ and $5$ at most $15$ times, is

May 4th, 2018, 05:26 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,609 Thanks: 845  
May 4th, 2018, 09:22 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 1,977 Thanks: 1026 
$\sum \limits_{k=0}^{15}~\dbinom{31}{k}\left(\dfrac 1 2\right)^{31} = \dfrac 1 2$


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