Here, `n=7p=0.25=1/4,q=1-1/4=3/4rge2`
where, `P(X)=""^(n)C_(r)(p)^(r )(q)^(n-r)`
In this case for easy approach we shall first find out the probability of his hitting almost once (i.e.,r=0,1) and then subtract this probability from 1 to get the desired probability.
`therefore P(X=r)=1-[P(r=0)+P(r=1)]`
`=1-[""^(7)C_(0)(1/4)^(0)(3/4)^(7-0)+""^(7)C_(1)(1/4)^(1)(3/4)^(7-1)]`
`=1-[(7!)/(0!7!)(3/4)^(7)+(7!)/(1!6!)(1/4)(3/4)^(6)]`
`=1-[(3/4)^(6)(3/4cdot1+1/4cdot7)]`
`=1-[(3^(6))/(4^(6))(10/4)]=1-[(3^(6)xx10)/(4^(7))]=1-[(27cdot27cdot10)/(64cdot256)]`
`=1-[(7290)/(16384)]=1-3645/8192=4547/8192`
