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May 4th, 2018, 03:12 AM  #1 
Senior Member Joined: Jul 2011 Posts: 402 Thanks: 16  probability problem
a Dice is thriwn $31$ times. Then probability of getting $2,4$ and $5$ at most $15$ times, is

May 4th, 2018, 06:26 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,791 Thanks: 970  
May 4th, 2018, 10:22 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,264 Thanks: 1198 
$\sum \limits_{k=0}^{15}~\dbinom{31}{k}\left(\dfrac 1 2\right)^{31} = \dfrac 1 2$


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