Question 375390
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Hi,
Note: The probability of x successes in n trials is: 

P = nCx* {{{p^x*q^(n-x)}}} where p and q are the probabilities of success and failure respectively. 
In this case p & q are = 1/2 or .5
nCx = {{{n!/(x!(n-x!))}}}  11C6 = 462    
P(exactly 6 surviving)=  462*(.5)^6(.5)^5 = .2256